In recent years, prediction models of radiation belt electron fluxes or phase space density have been established and optimized by numerical simulations and machine learning based on measurements near the geomagnetic equator. In the present work, using observations from low Earth orbit satellites, the Meteorological Operational Satellite Program of Europe-A (MetOp-A), we constructed a novel artificial neural network (ANN) model to predict the electron fluxes in low equatorial pitch angles at 40 and 130 keV. The historical solar wind and geomagnetic indices are adopted as model inputs. The ANN model achieves excellent performance in the main region of the outer radiation belt (L = 4–6), with overall root mean square errors of 0.3468 (0.3567), prediction efficiencies of 0.9381 (0.9343), and Pearson correlation coefficients of 0.8893 (0.8628) for electrons at 40 keV (130 keV). Moreover, 51.76% of samples for electrons at 40 keV exhibit an observation–prediction discrepancy of fewer than 0.2 orders of magnitude, 87.21% demonstrate a difference of less than 0.5 orders, and 98.58% show a difference of less than one order. For electrons at 130 keV, the three critical values are 51.29% for 0.2 order, 86.33% for 0.5 order, and 98.43% for one order. Moreover, the model can precisely monitor variations in radiation belt electron fluxes during a realistic geomagnetic storm event, with no substantial errors. By adopting observations in low Earth orbit, the present model concentrates on the electron fluxes in low equatorial pitch angles, which broadens the scope of the radiation belt electron forecast.

1.
X.
Li
,
D. N.
Baker
,
S. G.
Kanekal
,
M.
Looper
, and
M.
Temerin
, “
Long term measurements of radiation belts by SAMPEX and their variations
,”
Geophys. Res. Lett.
28
(
20
),
3827
3830
, https://doi.org/10.1029/2001GL013586 (
2001
).
2.
G. D.
Reeves
,
K. L.
McAdams
,
R. H. W.
Friedel
, and
T. P.
O'Brien
, “
Acceleration and loss of relativistic electrons during geomagnetic storms
,”
Geophys. Res. Lett.
30
(
10
),
1529
, https://doi.org/10.1029/2002GL016513 (
2003
).
3.
D. N.
Baker
,
S. G.
Kanekal
,
V. C.
Hoxie
,
M. G.
Henderson
,
X.
Li
,
H. E.
Spence
,
S. R.
Elkington
,
R. H.
Friedel
,
J.
Goldstein
,
M. K.
Hudson
,
G. D.
Reeves
,
R. M.
Thorne
,
C. A.
Kletzing
, and
S. G.
Claudepierre
, “
A long-lived relativistic electron storage ring embedded in Earth's outer Van Allen belt
,”
Science
340
(
6129
),
186
190
(
2013
).
4.
R. M.
Thorne
,
B.
Ni
,
X.
Tao
,
R. B.
Horne
, and
N. P.
Meredith
, “
Scattering by chorus waves as the dominant cause of diffuse auroral precipitation
,”
Nature
467
(
7318
),
943
946
(
2010
).
5.
B.
Ni
,
Z.
Zou
,
X.
Gu
,
C.
Zhou
,
R. M.
Thorne
,
J.
Bortnik
,
R.
Shi
,
Z.
Zhao
,
D. N.
Baker
,
S. G.
Kanekal
,
H. E.
Spence
,
G. D.
Reeves
, and
X.
Li
, “
Variability of the pitch angle distribution of radiation belt ultrarelativistic electrons during and following intense geomagnetic storms: Van Allen Probes observations
,”
JGR Space Phys.
120
(
6
),
4863
4876
(
2015
).
6.
Z.
Su
,
H.
Zhu
,
F.
Xiao
,
Q. G.
Zong
,
X. Z.
Zhou
,
H.
Zheng
,
Y.
Wang
,
S.
Wang
,
Y. X.
Hao
,
Z.
Gao
,
Z.
He
,
D. N.
Baker
,
H. E.
Spence
,
G. D.
Reeves
,
J. B.
Blake
, and
J. R.
Wygant
, “
Ultra-low-frequency wave-driven diffusion of radiation belt relativistic electrons
,”
Nat. Commun.
6
,
10096
(
2015
).
7.
Q. G.
Zong
,
Y. F.
Wang
,
H.
Zhang
,
S. Y.
Fu
,
H.
Zhang
,
C. R.
Wang
,
C. J.
Yuan
, and
I.
Vogiatzis
, “
Fast acceleration of inner magnetospheric hydrogen and oxygen ions by shock induced ULF waves
,”
J. Geophys. Res.
117
(
A11
),
A11206
, https://doi.org/10.1029/2012JA018024 (
2012
).
8.
Z.
Zou
,
P.
Zuo
,
B.
Ni
,
Z.
Gao
,
G.
Wang
,
Z.
Zhao
,
X.
Feng
, and
F.
Wei
, “
Two-step dropouts of radiation belt electron phase space density induced by a magnetic cloud event
,”
Astrophys. J. Lett.
895
(
1
),
L24
(
2020
).
9.
Z.
Zou
,
P.
Zuo
,
B.
Ni
,
J.
Wei
,
W.
Zhou
,
H.
Huang
, and
Y.
Xie
, “
Competition between the source and loss processes of radiation belt source, seed, and relativistic electrons induced by a magnetic cloud event
,”
Phys. Fluids
36
(
2
),
026603
(
2024
).
10.
D. L.
Turner
,
Y.
Shprits
,
M.
Hartinger
, and
V.
Angelopoulos
, “
Explaining sudden losses of outer radiation belt electrons during geomagnetic storms
,”
Nat. Phys.
8
(
3
),
208
212
(
2012
).
11.
D. L.
Turner
,
E. K. J.
Kilpua
,
H.
Hietala
,
S. G.
Claudepierre
,
T. P.
O'Brien
,
J. F.
Fennell
,
J. B.
Blake
,
A. N.
Jaynes
,
S.
Kanekal
,
D. N.
Baker
,
H. E.
Spence
,
J.-F.
Ripoll
, and
G. D.
Reeves
, “
The response of Earth's electron radiation belts to geomagnetic storms: Statistics from the van Allen probes era including effects from different storm drivers
,”
J. Geophys. Res. Space Phys.
124
(
2
),
1013
1034
, https://doi.org/10.1029/2018JA026066 (
2019
).
12.
K.-C.
Kim
and
D.-Y.
Lee
, “
Magnetopause structure favorable for radiation belt electron loss
,”
J. Geophys. Res. Space Phys.
119
(
7
),
5495
5508
, https://doi.org/10.1002/2014JA019880 (
2014
).
13.
Y. Y.
Shprits
,
N. P.
Meredith
, and
R. M.
Thorne
, “
Parameterization of radiation belt electron loss timescales due to interactions with chorus waves
,”
Geophys. Res. Lett.
34
(
11
),
L11110
, https://doi.org/10.1029/2006GL029050 (
2007
).
14.
Y. Y.
Shprits
,
D.
Subbotin
,
A.
Drozdov
,
M. E.
Usanova
,
A.
Kellerman
,
K.
Orlova
,
D. N.
Baker
,
D. L.
Turner
, and
K. C.
Kim
, “
Unusual stable trapping of the ultrarelativistic electrons in the Van Allen radiation belts
,”
Nat. Phys.
9
(
11
),
699
703
(
2013
).
15.
D. L.
Turner
,
V.
Angelopoulos
,
W.
Li
,
J.
Bortnik
,
B.
Ni
,
Q.
Ma
,
R. M.
Thorne
,
S. K.
Morley
,
M. G.
Henderson
,
G. D.
Reeves
,
M.
Usanova
,
I. R.
Mann
,
S. G.
Claudepierre
,
J. B.
Blake
,
D. N.
Baker
,
C.-L.
Huang
,
H.
Spence
,
W.
Kurth
,
C.
Kletzing
, and
J. V.
Rodriguez
, “
Competing source and loss mechanisms due to wave-particle interactions in Earth's outer radiation belt during the 30 September to 3 October 2012 geomagnetic storm
,”
J. Geophys. Res. Space Phys.
119
(
3
),
1960
1979
, https://doi.org/10.1002/2014JA019770 (
2014
).
16.
B.
Ni
,
J.
Liang
,
R. M.
Thorne
,
V.
Angelopoulos
,
R. B.
Horne
,
M.
Kubyshkina
,
E.
Spanswick
,
E. F.
Donovan
, and
D.
Lummerzheim
, “
Efficient diffuse auroral electron scattering by electrostatic electron cyclotron harmonic waves in the outer magnetosphere: A detailed case study
,”
J. Geophys. Res.
117
(
A1
),
A01218
, https://doi.org/10.1029/2011JA017095 (
2012
).
17.
J.
Bortnik
and
R. M.
Thorne
, “
The dual role of ELF/VLF chorus waves in the acceleration and precipitation of radiation belt electrons
,”
J. Atmos. Sol.-Terr. Phys.
69
(
3
),
378
386
(
2007
).
18.
X.
Cao
,
B.
Ni
,
D.
Summers
,
Z.
Zou
,
S.
Fu
, and
W.
Zhang
, “
Bounce resonance scattering of radiation belt electrons by low-frequency hiss: Comparison with cyclotron and landau resonances
,”
Geophys. Res. Lett.
44
(
19
),
9547
9554
, https://doi.org/10.1002/2017GL075104 (
2017
).
19.
J.
Li
,
J.
Bortnik
,
W.
Li
,
X.
An
,
L. R.
Lyons
,
W. S.
Kurth
,
G. B.
Hospodarsky
,
D. P.
Hartley
,
G. D.
Reeves
,
H. O.
Funsten
,
J. B.
Blake
,
H.
Spence
, and
D. N.
Baker
, “
Unraveling the formation region and frequency of chorus spectral gaps
,”
Geophys. Res. Lett.
49
(
19
),
e2022GL100385
, https://doi.org/10.1029/2022GL100385 (
2022
).
20.
X.
Cao
,
B.
Ni
,
D.
Summers
,
Y. Y.
Shprits
,
X.
Gu
,
S.
Fu
,
Y.
Lou
,
Y.
Zhang
,
X.
Ma
,
W.
Zhang
,
H.
Huang
, and
J.
Yi
, “
Sensitivity of EMIC wave-driven scattering loss of ring current protons to wave normal angle distribution
,”
Geophys. Res. Lett.
46
(
2
),
590
598
, https://doi.org/10.1029/2018GL081550 (
2019
).
21.
D.
Summers
, “
Quasi-linear diffusion coefficients for field-aligned electromagnetic waves with applications to the magnetosphere
,”
J. Geophys. Res.
110
(
A8
),
A08213
, https://doi.org/10.1029/2005JA011159 (
2005
).
22.
J. M.
Albert
, “
Refractive index and wavenumber properties for cyclotron resonant quasilinear diffusion by cold plasma waves
,”
Phys. Plasmas
14
(
7
),
072901
(
2007
).
23.
M.
Hua
,
W.
Li
,
B.
Ni
,
Q.
Ma
,
A.
Green
,
X.
Shen
,
S. G.
Claudepierre
,
J.
Bortnik
,
X.
Gu
,
S.
Fu
,
Z.
Xiang
, and
G. D.
Reeves
, “
Very-Low-Frequency transmitters bifurcate energetic electron belt in near-Earth space
,”
Nat. Commun.
11
(
1
),
4847
(
2020
).
24.
Z. L.
Gao
,
X. J.
Shang
,
P. B.
Zuo
,
Z. Y.
Zou
,
G.
Wang
,
X. S.
Feng
,
Y.
Wang
,
C. Y.
Guan
, and
F. S.
Wei
, “
Lag-correlated rising tones of electron cyclotron harmonic and whistler-mode upper-band chorus waves
,”
Phys. Plasmas
27
(
6
),
062903
(
2020
).
25.
Z.
Zou
,
P.
Zuo
,
B.
Ni
,
F.
Wei
,
Z.
Zhao
,
X.
Cao
,
S.
Fu
, and
X.
Gu
, “
Wave normal angle distribution of fast magnetosonic waves: A survey of van Allen probes EMFISIS observations
,”
JGR Space Phys.
124
(
7
),
5663
5674
(
2019
).
26.
Z.
He
,
J.
Yu
,
L.
Chen
,
Z.
Xia
,
W.
Wang
,
K.
Li
, and
J.
Cui
, “
Statistical study on locally generated high-frequency plasmaspheric Hiss and its effect on suprathermal electrons: Van Allen probes observation and quasi-linear simulation
,”
J. Geophys. Res. Space Phys.
125
(
10
),
e2020JA028526
, https://doi.org/10.1029/2020JA028526 (
2020
).
27.
Z.
He
,
J.
Yu
,
K.
Li
,
N.
Liu
,
Z.
Chen
, and
J.
Cui
, “
A comparative study on the distributions of incoherent and coherent plasmaspheric hiss
,”
Geophys. Res. Lett.
48
(
7
),
e2021GL092902
, https://doi.org/10.1029/2021GL092902 (
2021
).
28.
B.
Ni
,
J.
Bortnik
,
R. M.
Thorne
,
Q.
Ma
, and
L.
Chen
, “
Resonant scattering and resultant pitch angle evolution of relativistic electrons by plasmaspheric hiss
,”
JGR Space Phys.
118
(
12
),
7740
7751
(
2013
).
29.
D.
Wang
,
Y. Y.
Shprits
,
I. S.
Zhelavskaya
,
F.
Effenberger
,
A. M.
Castillo
,
A. Y.
Drozdov
,
N. A.
Aseev
, and
S.
Cervantes
, “
The effect of plasma boundaries on the dynamic evolution of relativistic radiation belt electrons
,”
J. Geophys. Res. Space Phys.
125
(
5
),
e2019JA027422
, https://doi.org/10.1029/2019JA027422 (
2020
).
30.
D.
Wang
,
Y. Y.
Shprits
,
B.
Haas
, and
A. Y.
Drozdov
, “
Improved lifetime model of energetic electrons due to their interactions with chorus waves
,”
Geophys. Res. Lett.
51
(
19
),
e2023GL107991
, https://doi.org/10.1029/2023GL107991 (
2024
).
31.
Y. Y.
Shprits
,
A. Y.
Drozdov
,
M.
Spasojevic
,
A. C.
Kellerman
,
M. E.
Usanova
,
M. J.
Engebretson
,
O. V.
Agapitov
,
I. S.
Zhelavskaya
,
T. J.
Raita
,
H. E.
Spence
,
D. N.
Baker
,
H.
Zhu
, and
N. A.
Aseev
, “
Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts
,”
Nat. Commun.
7
,
12883
(
2016
).
32.
B.
Ni
,
Y.
Shprits
,
T.
Nagai
,
R.
Thorne
,
Y.
Chen
,
D.
Kondrashov
, and
H.
Kim
, “
Reanalyses of the radiation belt electron phase space density using nearly equatorial CRRES and polar-orbiting Akebono satellite observations
,”
J. Geophys. Res.
114
(
A5
),
A05208
, https://doi.org/10.1029/2008JA013933 (
2009
).
33.
J.
Bortnik
and
R. M.
Thorne
, “
Transit time scattering of energetic electrons due to equatorially confined magnetosonic waves
,”
J. Geophys. Res.
115
(
A7
),
A07213
, https://doi.org/10.1029/2010JA015283 (
2010
).
34.
B.
Ni
,
R.
Thorne
,
J.
Liang
,
V.
Angelopoulos
,
C.
Cully
,
W.
Li
,
X.
Zhang
,
M.
Hartinger
,
O.
Le Contel
, and
A.
Roux
, “
Global distribution of electrostatic electron cyclotron harmonic waves observed on THEMIS
,”
Geophys. Res. Lett.
38
(
17
),
L17105
, https://doi.org/10.1029/2011GL048793 (
2011
).
35.
J.
Bortnik
,
W.
Li
,
R. M.
Thorne
, and
V.
Angelopoulos
, “
A unified approach to inner magnetospheric state prediction
,”
JGR Space Phys.
121
(
3
),
2423
2430
(
2016
).
36.
J.
Bortnik
,
X.
Chu
,
Q.
Ma
,
W.
Li
,
X.
Zhang
,
R. M.
Thorne
,
V.
Angelopoulos
,
R. E.
Denton
,
C. A.
Kletzing
,
G. B.
Hospodarsky
,
H. E.
Spence
,
G. D.
Reeves
,
S. G.
Kanekal
, and
D. N.
Baker
, “
Artificial neural networks for determining magnetospheric conditions
,” in
Machine Learning Techniques for Space Weather
, edited by
E.
Camporeale
,
S.
Wing
, and
J. R.
Johnson
(
Elsevier
,
2018
), Chap. 11, pp.
279
300
.
37.
X.
Chu
,
D.
Ma
,
J.
Bortnik
,
W. K.
Tobiska
,
A.
Cruz
,
S. D.
Bouwer
,
H.
Zhao
,
Q.
Ma
,
K.
Zhang
,
D. N.
Baker
,
X.
Li
,
H.
Spence
, and
G.
Reeves
, “
Relativistic electron model in the outer radiation belt using a neural network approach
,”
SPACE Weather Int. J. Res. Appl.
19
(
12
),
e2021SW002808
(
2021
).
38.
Y.
Chen
,
G. D.
Reeves
,
X.
Fu
, and
M.
Henderson
, “
PreMevE: New predictive model for megaelectron-volt electrons inside Earth's outer radiation belt
,”
Space Weather
17
(
3
),
438
454
, https://doi.org/10.1029/2018SW002095 (
2019
).
39.
R.
Pires de Lima
,
Y.
Chen
, and
Y.
Lin
, “
Forecasting megaelectron-volt electrons inside Earth's outer radiation belt: PreMevE 2.0 based on supervised machine learning algorithms
,”
Space Weather
18
,
1
23
, https://doi.org/10.1029/2019SW002399 (
2020
).
40.
S. G.
Claudepierre
and
T. P.
O'Brien
, “
Specifying high-altitude electrons using low-altitude LEO systems: The SHELLS model
,”
Space Weather Int. J. Res. Appl.
18
(
3
),
e2019SW002402
(
2020
).
41.
Q.
Yuan
,
Z.
Zou
,
W.
San
,
J.
Hu
, and
B.
Zhu
, “
Predicting radiation belt relativistic electron flux from sub-relativistic electron fluxes using machine learning
,”
Phys. Fluids
37
(
2
),
026618
(
2025
).
42.
Z.
Zou
,
L.
Zhang
,
P.
Zuo
,
W.
San
,
Q.
Yuan
,
B.
Zhu
, and
J.
Hu
, “
Global prediction of sub-relativistic and relativistic electron fluxes in the geosynchronous orbit using artificial neural networks
,”
Phys. Fluids
36
(
12
),
126638
(
2024
).
43.
W.
San
,
Z.
Zou
,
Q.
Yuan
,
J.
Hu
, and
B.
Zhu
, “
Prediction of radiation belt relativistic electron phase space density using artificial neural networks
,”
Phys. Fluids
37
(
1
),
016615
(
2025
).
44.
Z. Y.
Zou
,
Y. Y.
Shprits
,
B. B.
Ni
,
N. A.
Aseev
,
P. B.
Zuo
, and
F. S.
Wei
, “
An artificial neural network model of electron fluxes in the Earth's central plasma sheet: A THEMIS survey
,”
Astrophys. Space Sci.
365
(
6
),
100
(
2020
).
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