Space weather and hurricanes Irma, Jose and Katia

Abstract

This research is devoted to the determination of the causal relationship between the flow of particles that are coming from the Sun and the hurricanes Irma, Jose, and Katia. To accomplish this, the lag correlation analysis was performed. High correlation coefficients confirmed a preliminary conclusion about the relationship between solar activities and the hurricane phenomenon, which allows further research. Five parameters i.e. characteristics of solar activity (10.7 cm solar radio flux (F10.7), the flows of protons and electrons with maximum energy, speed and density of solar wind particles) were chosen as model input, while the wind speed and air pressure of Irma, Jose, and Katia hurricanes were used as model output. Input data were sampled to a six hours interval in order to adapt the time interval to the observed data about hurricanes, in the period between September 28 and December 21, 2017. As a result of the preliminary analysis, using 12,274,264 linear models by parallel calculations, six of them were chosen as best. The identified lags were the basis for refinement of models with the artificial neural networks. Multilayer perceptrons with back propagation and recurrent LSTM have been chosen as commonly used artificial neural networks. Comparison of the accuracy of both linear and artificial neural networks results confirmed the adequacy of these models and made it possible to take into account the dynamics of the solar wind. Sensitivity analysis has shown that F10.7 has the greatest impact on the wind speed of the hurricanes. Despite low sensitivity of pressure to change the parameters of the solar wind, their strong fluctuations can cause a sharp decrease in pressure, and therefore the appearance of hurricanes.

Full text

Astrophys Space Sci (2019) 364:154
https://doi.org/10.1007/s10509-019-3646-5
ORIGINAL ARTICLE
Space weather and hurricanes Irma, Jose and Katia
Yaroslav Vyk lyuk1,2 ·MilanM.Radovanovi´
c3,4 ·Boško Milovanovi´
c3·Milan Milenkovi´
c3·Marko Petrovi´
c3,4 ·
Dejan Doljak3·Slavica Malinovi´
cMili´
cevi´
c5·Natalia Vukovi´
c6·Aleksandra Vujko7·Nataliia Matsiuk8·
Saumitra Mukherjee9
Received: 10 January 2019 / Accepted: 10 September 2019
© Springer Nature B.V. 2019
Abstract This research is devoted to the determination of
the causal relationship between the flow of particles that are
coming from the Sun and the hurricanes Irma, Jose, and Ka-
tia. To accomplish this, the lag correlation analysis was per-
formed. High correlation coefficients confirmed a prelimi-
nary conclusion about the relationship between solar activi-
ties and the hurricane phenomenon, which allows further re-
search. Five parameters i.e. characteristics of solar activity
(10.7 cm solar radio flux (F10.7), the flows of protons and
electrons with maximum energy, speed and density of solar
wind particles) were chosen as model input, while the wind
speed and air pressure of Irma, Jose, and Katia hurricanes
BD. Doljak
d.doljak@gi.sanu.ac.rs
1Institute of Laser and Optoelectronic Intelligent Manufacturing,
College of Mechanical and Electrical Engineering, Wenzhou
University, Wenzhou 325035, P.R. China
2Bukovinian University, Darvina str. 2A, Chernivtsi 58000,
Ukraine
3Geographical Institute “Jovan Cviji´
c”, Serbian Academy of
Sciences and Arts, Djure Jakši´
ca 9, 11000 Belgrade, Serbia
4Institute of Sports, Tourism and Service, South Ural State
University, Soni Krivoi str., 60, Chelyabinsk 454080, Russia
5University Center for Meteorology and Environmental
Modelling, University of Novi Sad, Dr Zorana Djindji´
ca 1, 21000
Novi Sad, Serbia
6Graduate School of Economics and Management, The Ural
Federal University Named after the First President of Russia B.N.
Yeltsin, 19 Mira St., Yekaterinburg 620002, Russia
7Novi Sad Business School, Vladimira Peri´
ca Valtera 4, 21000
Novi Sad, Serbia
8Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi
Str. Chernivtsi 58012, Ukraine
9School of Environmental Sciences, Jawaharlal Nehru University,
New Delhi 110067, India
were used as model output. Input data were sampled to a six
hours interval in order to adapt the time interval to the ob-
served data about hurricanes, in the period between Septem-
ber 28 and December 21, 2017. As a result of the prelim-
inary analysis, using 12,274,264 linear models by parallel
calculations, six of them were chosen as best. The identi-
fied lags were the basis for refinement of models with the
artificial neural networks. Multilayer perceptrons with back
propagation and recurrent LSTM have been chosen as com-
monly used artificial neural networks. Comparison of the ac-
curacy of both linear and artificial neural networks results
confirmed the adequacy of these models and made it possi-
ble to take into account the dynamics of the solar wind. Sen-
sitivity analysis has shown that F10.7 has the greatest impact
on the wind speed of the hurricanes. Despite low sensitivity
of pressure to change the parameters of the solar wind, their
strong fluctuations can cause a sharp decrease in pressure,
and therefore the appearance of hurricanes.
Keywords Charged particles ·Atmospheric disturbances ·
Artificial neural network ·Hurricanes
1 Introduction
The solar proton anomaly and its impact on the Earth has im-
proved the understanding of environment changes induced
by the Sun (Mukherjee 2013). Sudden changes in the ter-
restrial temperature have some bearing with the proton flux
anomaly (Mukherjee 2015). At the end of August and begin-
ning of September 2017, the instruments on the Advanced
Composition Explorer (ACE) satellite measured the unusu-
ally strong flow of high-energy particles. Then, in the geo-
effective position, there was a coronary hole rising from
the northern polar region of the Sun across its equator, as

154 Page 2 of 15 Y. Vyklyuk et al.
well as the energy regions 12671 and 12672 (SolarMoni-
tor.org 2017). The satellite is otherwise located in the La-
grange point so that in real time it measures the parameters
of the solar wind (SW). During the first half of September,
more than a dozen M-class flashes, an X-9 level flare and an
associated moderate solar particle event (SPE) appeared in
the geo-effective position. On September 7 and 8, 2017, the
early arrival of the coronal mass ejection (CME) associated
with the X-9 flare produced severe geomagnetic storming.
Simultaneously with these processes in the Sun, in the at-
mosphere over the Atlantic, some disturbances developed
into the hurricanes Irma, Jose, and Katia, where Irma was
one of the most devastating hurricanes ever recorded (Japan
Aerospace Exploration Agency Earth Observation Research
Center 2017).
It can be said that there are numerous concerns about
both the occurrence of cyclone disorders and their behav-
ior in time and space (Frank and Young 2007). The analysis
of surface pressure variations after SPEs and Forbush de-
creases for the Eurasian region has shown significant varia-
tions of this atmospheric pressure during at least the first five
days after the events. These variations differ alongside lati-
tude and longitude. There are cells of increased and reduced
surface pressure (Morozova et al. 2002; Mihajlovi´
c2017).
Hodges et al. (2014), Radovanovi´
c(2018) bring a list
of references that verify the idea of the causal-consequence
link of processes in the Sun with hurricanes, dating back to
the 19th century.
A spatially heterogeneous response in hurricane intensity
and frequency is observed in response to changes in solar
activity (Elsner et al. 2008). Hodges and Elsner (2012)ar-
gued that regional hurricane frequency from 1851 to 2010
indicates fewer hurricanes across the Caribbean and along
the eastern seaboard of the USA when sunspots are numer-
ous. In contrast, fewer hurricanes are observed in the central
and eastern North Atlantic when sunspots are few. A sig-
nificant positive correlation between the averaged Kp index
of global geomagnetic activity and hurricane intensity as
measured by maximum sustained wind speed is identified
for baroclinically-initiated hurricanes (Elsner and Kavlakov
2001).
Solar radiation has an important influence on the entire
Earth’s atmosphere (Bajˇ
ceti´
cetal.2015; Todorovi´
c Drakul
et al. 2016). It has been long noted that the solar-associated
climate anomalies in the troposphere are largely of strato-
spheric origin (Haigh 1996). It is observed that significant
weather events, particularly if caused by low pressure sys-
tems, tend to follow arrivals of the high-speed solar wind
(Prikryl et al. 2017). Previously published statistical evi-
dence that explosive extratropical cyclones in the northern
hemisphere tend to occur within a few days after arrivals of
high-speed solar wind streams from coronal holes (Prikryl
et al. 2009a,b,2016) is corroborated for the southern hemi-
sphere.
It has been found that solar cosmic ray bursts result in an
increase in the duration of elementary synoptic processes in
the Atlantic–European sector of the Northern Hemisphere.
It has been assumed that the observed variations in the el-
ementary synoptic processes duration are caused by the ef-
fect of short period cosmic ray variations on the intensity
of cyclonic processes at middle and high latitudes (Verete-
nenko and Thejll 2004; Artamonova and Veretenenko 2013;
Veretenenko 2017).
Applying wavelet spectral analysis to the hurricane time
series, Mendoza and Pazos (2009) found periodicities that
coincide with the main sunspot and magnetic solar cycles.
In the Atlantic Ocean, there are peaks near 11 and 22 years.
Their results indicate that the highest significant correlations
are found between the Atlantic and Pacific hurricanes and
the Dst index. Most importantly, both oceans present the
highest hurricane – Dst correlations during the ascending
part of odd solar cycles and the descending phase of even
solar cycles.
First, we could say, surprisingly successful forecasts
were published by P. Corbyn for 6–11 months in advance.
The methods he used were related solely to variations in the
behavior of the Sun, its magnetic field, coronal eruptions,
and fluctuating character of the solar wind. The result was
that in the period from October 1995 to September 1997,
four out of five strong storms were accurately forecasted.
The fifth one had an error of 48 hours (Wheeler 2001).
Vyklyuk et al. (2017a) have tried, using the ANFIS
model, to determine if there is a mathematical connection
between the flow of high energy particles from the Sun and
the number of hurricanes. For the period 1999–2013 (daily
values from May to October), with a phase shift of 0–3 days,
it was found that the models can explain at best 22%–26%
of the potential connectivity. In another attempt, Vyklyuk
et al. (2017b), for the same period, used better computer
equipment and extended the phase shift from 0–10 days,
which obtained better results (up to 39%). The authors con-
clude that these results cannot be ignored and that additional
efforts are needed to explain the cause-and-effect relation-
ships. In that sense, we considered that it would also be nec-
essary to examine the causal relationship between the flow
of particles from the Sun and the formation of hurricanes
Irma, Katia, and Jose.
Unlike the mentioned studies where the period from
1999–2013 was processed, in this paper, the focus is on three
specific cases, i.e. establish a possible cause-consequential
connection with certain examples, where the event times
overlap and refer to the interval up to 16 days. Consider-
ing that the implementation of the appropriate procedures
has concluded that on a long-term basis a certain connection
exists, it was challenging to apply the same methods, in or-
der to investigate which results can be obtained for a period
of few weeks.

Space weather and hurricanes Irma, Jose and Katia Page 3 of 15 154
Table 1 The main
characteristics of the
investigated hurricanes
Irma Jose Katia
The beginning 30 Aug. 2017
at 12:00 UTC
5 Sep. 2017
at 12:00 UTC
5 Sep. 2017
at 18:00 UTC
The end 12 Sep. 2017
at 00:00 UTC
21 Sep. 2017
at 18:00 UTC
9 Sep. 2017
at 20:00 UTC
Date of maximum wind speed 6 Sep. 2017
at 6:00 UTC
9 Sep. 2017
at 11:00 UTC
8 Sep. 2017
at 18:00 UTC
Duration 13 days 16 days 4 days
Sampling 6 hr 6 hr 6 hr
Number of observations 52 66 15
2 Input data analysis
The Unisys (2017) was the source of data on hurricanes
Irma, Jose, and Katia. The data included maximum sus-
tained winds in knots, and central pressure in millibar (mb)
for periods of 6 hours (0–6 hr, 6–12 hr, 12–18 hr, and
18–24 hr). The 5-minute data on solar particle and elec-
tron fluxes (source: GOES-15) were provided by the Space
Weather Prediction Center (2017a). The particles are pro-
tons (P) at >1MeV,>5MeV,>10 MeV, >30 MeV,
>50 MeV, and >100 MeV. The data on electrons (E) in-
cluded >0.8 MeV and >2.0 MeV. The source of daily so-
lar F10.7 cm (2 800 MHz) was the Space Weather Predic-
tion Center (2017b). The data on proton speed (km/s) and
proton density (protons per cubic centimetre) were obtained
from the data archive of the SOHO CELIAS Proton Monitor
(2017).
The task was to find functional dependencies between the
solar wind (SW) parameters and the main characteristics of
hurricanes. The main characteristics of the dataset are shown
in Table 1. The main investigated criteria (like output) were
the speed of wind and pressure. As one can see from Table 1,
the data for each hurricane were updated every 6 hours.
Each record represents an averaged metric for the spec-
ified sampling interval. The dynamics of the mentioned
above characteristics are shown in Fig. 1a and 1b.
As can be seen in Fig. 1a, each hurricane has a pro-
nounced peak (black arrows) in the wind speed graph. Each
of these peaks, accordingly to the Bernoulli’s law, corre-
sponded to the minimum pressure at the hurricane epicenter.
It is also clear that these hurricanes reached their maximum
wind speed with a difference of 1–3 days. So we can assume
that they are caused by the same factors. As was shown in
the paper (Vyklyuk et al. 2017a), the parameters of solar ac-
tivity can be used as approximations of these factors.
3 Preliminary processing of input data
The characteristics of SW which were tested in the work
(like input parameters) include flows of protons and elec-
trons of different energies, a complex indicator of solar wind
– 10.7, speed and density of the particles of SW. The main
characteristics of the set of input data are given in Table 2.
As one can see from Table 2, the range of input parame-
ters is greater than that of the output ones. It allows us to take
into account lag dependencies without reducing the num-
ber of the time series. It should be noted that the sampling
of measurement of values in all cases except for F10.7 is
greater than the studied output values (see Table 1). In fur-
ther research the sampling of all input data was reduced to
six hours by averaging:
In(ti)=
i−1

j=i−b
In(tj)/b, (1)
where In is time series of the input parameter, bis the num-
ber of averaged data, and jis moment (index of record) of
time in the time series.
The averaging was made taking into account that the
value at a given moment In(tj)is averaged over the en-
tire previous period between measurements, not including
measurements at a given time. In the case of time series of
electrons and protons, the value of blocks of averaged data
was b=72. Respectively for speed and wind density: b=6.
This averaging helped to eliminate the problem of missing
data, which was sometimes observed in time series.
In the case of the F10.7 time series, whose sampling is
greater than the output fields, the data were interpolated with
a sampling of 6 hours. The cubic spline interpolation using
Hermite polynomials (PCHIP) was used (Fritsch and Carl-
son 1980). Interpolation results are presented in Fig. 2.
As can be seen from Fig. 2, the graph has no oscillations
but has pronounced extrema at points 4 and 7 September
2017. This is ahead of the peaks of studied hurricanes, from
two to five days, respectively. So, in order to take into ac-
count the influence of these two peaks, in case of finding the
relationship between this factor and the output fields, the lag
delay can be equal from 8 to 20 six-hour intervals.

154 Page 4 of 15 Y. Vyklyuk et al.
Fig. 1 Wind speed (a) and
pressure (b) for hurricanes Irma,
Jose and Katia. Black arrows
represent dates of the maximum
wind speed and minimum air
pressure, respectively
Table 2 Characteristics of the SW set
The characteristics of
solar activity
Units of
measurement
The beginning The end Sampling
P>1, P>5, P>10,
P>30, P>50, and
P>100
Protons
(>MeV)/(cm2·s)
28 Aug. 2017
at 00:00 UTC
22 Sep. 2017
at 00:00 UTC
5min
E>0.8andE>2.0 Electrons
(>MeV)/(cm2·s)
28 Aug. 2017
at 00:00 UTC
22 Sep. 2017
at 00:00 UTC
5min
F10.7 28 Aug. 2017 at
00:00 UTC
21 Sep. 2017
at 00:00 UTC
1day
Proton speed km/s 28 Aug. 2017
at 00:00 UTC
22 Sep. 2017
at 00:00 UTC
1 hour
Proton density Protons/cm328 Aug. 2017
at 00:00 UTC
22 Sep. 2017
at 00:00 UTC
1 hour
4 Correlation analysis
To find the relationship between input factors, a correlation
analysis (Cohen et al. 2013) was carried out (see Table 3).
As can be seen from Table 3, there is a strong correlation
between the time series of proton flows. The situation is the
same for the electron flows. So, the number of input factors
can be significantly reduced. In order to select the most ap-
propriate factor, the time series was normalized and depicted
on a single graph (Fig. 3a, 3b, and 3c).
As can be seen from Fig. 3a, all normalized factors that
describe the flow of protons are characterized by the same
dynamics. Namely, all 6 time series have two distinct peaks.
The first peak corresponds to the date September 7, 2017, the
second to September 11, 2017. Namely, the first came later
after the wind speed extreme hurricane Irma and somewhat
ahead of the hurricanes Jose and Katia. The second peak
appears after all three hurricanes, so it is unlikely that the
flow of protons affects the appearance of hurricanes.
As can be seen from Fig. 3b, the behavior of electron
fluxes of different energies is quite similar. There are pro-
nounced oscillations on the graphs that are not visually ob-
served in the dynamics of studied characteristics of hurri-
canes. The behavior of the SW (Fig. 3c) also significantly
differs from Fig. 1. That is why there is a low probability of
influence of these factors on the wind power and hurricane
air pressure.
To confirm or refute these conclusions a lag correlation
analysis was conducted, which allowed to find a correlation
between the separate time series of input factors displaced
for a certain number of rows vertically down (lag) and output
factors (Olden and Neff 2001). The lag was investigated in

Space weather and hurricanes Irma, Jose and Katia Page 5 of 15 154
Fig. 2 Interpolation of F10.7 for
sampling of 6 hours
Table 3 Correlation analysis of input factors
P>1P>5P>10 P >30 P >50 P >100 E >0.8 E >2.0 Speed Density F10.7
P>11.00
P>50.77 1.00
P>10 0.66 0.97 1.00
P>30 0.56 0.91 0.98 1.00
P>50 0.52 0.87 0.95 0.99 1.00
P>100 0.45 0.78 0.87 0.94 0.98 1.00
E>0.8 −0.19 −0.12 −0.05 0.01 0.03 0.06 1.00
E>2.0 −0.20 −0.17 −0.12 −0.09 −0.07 −0.06 0.81 1.00
Speed 0.26 0.11 0.09 0.07 0.07 0.07 0.13 0.02 1.00
Density 0.27 0.13 0.09 0.07 0.06 0.04 −0.38 −0.19 0.00 1.00
F10.7 0.12 −0.04 −0.15 −0.20 −0.19 −0.16 −0.07 −0.22 −0.11 −0.10 1.00
the range from 0 to 20 sampling (5 days). The results of
the analysis of the maximum and minimum values of the
correlation coefficient depending on the lag are represented
in Table 4.
Calculations show that errors consist only 8–10% of cor-
relation coefficients absolute values. As can be seen from
Table 4, the highest correlation coefficient Ris observed for
the factor F10.7 for the Irma hurricane: Rwind speed =0.86
(lag =6), Rpr =−0.91 – pressure (lag =9). Then Katia
(lag =17)R
wind speed =0.84, and Rpr =−0.91. The hur-
ricane Jose has the smallest correlation coefficient (lag =
18) Rwind speed =0.72 and Rpr =−0.47. Negative values of
correlation coefficients for pressure time series prove an in-
verse relationship between the input factor and the output
one. This confirms the preliminary conclusions about the re-
lationship between this factor and hurricane parameters.
As results from Table 4show, that taking into account lag
shift of time series, correlation coefficients of other factors
essentially increased, including the electron flux and char-
acteristics of the SW. The flow of protons has a high cor-
relation coefficient only for the Katia hurricane. This may
be explained due to a small number of observations for this
hurricane (Table 1). To establish the functional dependence
of this, further analysis is required. In the absence of a phys-
ical hypothesis and the availability only time series, the best
approximation is the Data Mining approach.
In addition, the distribution of lags with maximum (min-
imum) correlation coefficients is significant for different in-
put variables. Thus, high correlation coefficients and the un-

154 Page 6 of 15 Y. Vyklyuk et al.
Fig. 3 Normalized input
parameters of proton flows (a),
electron flows (b), speed,
density, and F(c)
Table 4 Consolidated correlation lag analysis of input factors
P>1P>5P>10 P >30 P >50 P >100 E >0.8 E >2.0 Speed Density F10.7
Wind speed of the Irma hurricane
Max 0.21 0.37 0.33 0.20 0.20 0.18 0.73 0.54 0.39 0.07 0.86
Lag667 7 7 9 1413207 6
Pressure of the Irma hurricane
Min −0.38 −0.46 −0.43 −0.33 −0.33 −0.22 −0.81 −0.61 −0.51 0.03 −0.91
Lag767 7 7 9 1414207 9
Wind speed of the Jose hurricane
Max 0.44 0.13 0.12 0.13 0.14 0.16 0.18 0.21 0.45 0.15 0.72
Lag700 0 0 0 202031218
Pressure of the Jose hurricane
Min −0.37 −0.02 −0.02 −0.07 −0.09 −0.11 −0.33 −0.25 −0.53 −0.24 −0.47
Lag 7 10 0 0 0 0 0 20 4 12 19
Wind speed of the Katia hurricane
Max 0.55 0.57 0.65 0.68 0.62 0.74 0.68 0.61 0.66 0.51 0.84
Lag 0 9 11 2 12 11 19 19 0 1 17
Pressure of the Katia hurricane
Min −0.58 −0.70 −0.68 −0.76 −0.65 −0.77 −0.76 −0.68 −0.71 −0.53 −0.91
Lag19112 2 11 191901 17
resolved issue of lags cause further research to find func-
tional relationships between these input and output param-
eters. Therefore, F10.7, the flows of protons and electrons
with maximum energy (P >100 and E >2.0) and speed
and density of solar wind particles were selected as test pa-
rameters for the further research.
5 Parallel calculations for finding optimal
models
For easy formalization of the models, we combine the output
time series into a target vector and the input parameters into

Space weather and hurricanes Irma, Jose and Katia Page 7 of 15 154
a vector of parameters:
T=(T1,T
2,T
3,T
4,T
5,T
6), (2)
X=(X1,X
2,X
3,X
4,X
5), (3)
where Tiis the time series of the wind speed and pressure of
Irma, Jose, and Katia hurricanes, respectively; Xjis the time
series of P >100, E >2.0, speed of solar wind particles,
density of solar wind particles, and F10.7, respectively.
The task is to find for each Tithe most accurate and ade-
quate functional dependence of the type:
Ti=Fi(X, Li,Ω
i), (4)
where Li={lij}j=1,5is the vector of optimal lags and Ωi
is a parameter of the linear or the artificial neural network
model.
The determination coefficient (R2) and mean square error
(MSE) were considered as criteria of optimization. As fur-
ther calculations have shown, in most cases the model with
the maximum determination coefficient and the minimum
mean square error coincided. In the case of differences in
these models, models with the maximum value of the deter-
mination coefficient were more adequate. Therefore, further
research usesed the determination coefficient as a criterion
of adequacy.
Cross-validation (cv)fork-blocks (k-fold) was used to
verify the accuracy of the models (Trippa et al. 2015). The
training sample was divided into kblocks of the same size.
Each block alternately was as a test sample, and the other
k−1 blocks were a training sample. The goal function of op-
timization model was to maximize the determination coef-
ficient R2
ibetween target vector Tiand the cross-validation
results of model Fcv
i(X, Li,Ω
i). Test calculations show that
the best accuracy was obtained where the size of the test
sample was 10% of the total size of the training sample, i.e.
k=10. In general, the optimization problem has the form:
R2
i(Ti,Fcv
i(X, Li,Ω
i)) yields
−→ max (5)
Solution variables: Li∈Ts,Ω
i
Limitations:
{lij}j=1−5≤Lagmax,
where Ωiis the parameters of the model, which are deter-
mined by fitting the initial model data to the target vector, the
fitting method depends on the type of model (linear, neural
network, etc.). Ts – set of vector Lilag combinations.
The optimization was done by completely scanning all
possible combinations of the lag vector Lifor each compo-
nent of vector Xfrom 0 to 22 (Lagmax =22). The magnitude
of the maximum lag was chosen from the preliminary analy-
sisofTable4, where the maximum lag was 20. Therefore, it
was decided to check two lags more. The total number of all
possible combinations of lags consists of 235=6,436,343.
Where 5 – numbers of vector Xcomponents. The all possi-
ble lag combinations Ts is defined as a set of tuples:
Ts(22)=tst1
1,tst2
2,tst3
3,tst4
4,tst5
5t1,t2,t 3,t4,t 5=0−22,(6)
where tstj
j– the value of lag for components of Livector.
For cross-validation, it is necessary to optimize each
model 10 times plus one additional for a full set of values of
the training sample. Such optimization should be performed
for each element of the target vector, which is six. With this
in mind, the total number of models that need to be opti-
mized will be: 235·11 ·6=424,798,638. Such a huge num-
ber of tasks requires an optimal choice for both the type of
model (see Eq. (4)) and optimization algorithms.
In order to reduce the number of tested lags, an algorithm
for finding an optimal model was proposed:
1. The first maximum number of lags is determined by
lag =0.
2. A set of tasks is formed based on Eq. (6).
3. For the first run Ta sks (lag).
4. For next runs in order to avoid repetitions of tasks the
difference of sets needs to be calculated Tas ks(lag)=
Tasks(lag)\Ta sks(lag-1).
5. The optimal model is found according to Eq. (5).
6. If the maximum lag value for any component of the op-
timal model does not exceed lag-2, it is assumed that the
optimal value is found and the algorithm is completed.
7. If lag =22, the algorithm is completed and is considered
to have no optimal value.
8. Increase lag+=1 and move to step 1.
The presence of the set of several independent tasks
which use the same memory area makes it possible to use
parallel calculations by forming a pool for multiprocessing
tasks, according to Eq. (5). The task with a specific tuple of
lags was alternately selected from the pool and sent to the
free core of the processor “worker” for calculation. After
calculating all tasks, a function with a maximum determina-
tion coefficient was found and the conditions 4 and 5 of the
algorithm were checked (Palach 2014).
Linear models were selected as test cases. Combination
of the proposed algorithm and parallel calculation allowed
us to reduce calculation time, about 10 times, and determi-
nation of optimal lags for each of the input parameters for
all goal vectors.
6 Refinement of models using artificial
neural networks
As a result of the preliminary analysis, six linear models are
obtained using Eq. (4). That is why the parameters of linear

154 Page 8 of 15 Y. Vyklyuk et al.
models ΩiTand the lags of input parameters Liare known.
The identified lags were the basis for refinement of models
with the artificial neural networks. As can be seen from Ta-
ble 1, the maximum size of the training samples is 66, and
a minimum is 15 records. Each neural network must have
an input layer comprised of five neurons. Such a small size
of the training sample puts some restrictions on the size of
neural networks and the possibility of their adequate train-
ing. Multilayer perceptrons (MLPs) with back propagation
were chosen (Géron 2017). The method of training was as
a quasi-Newtonian method of optimization. A logistic func-
tion was selected as an activation function.
As test calculations have shown, the best results were ob-
served for single-layered neural networks with the number
of neurons in a hidden layer, which equals seven. Decreas-
ing the number of neurons in the hidden layer reduced the
network’s ability to learn. Increasing the number of neu-
rons in the hidden layer, on the contrary, led to retraining.
Namely, on the one hand, the results of learning on the train-
ing set have improved significantly, but on the other side,
significant fluctuations in the results of the cross-validation
test appeared. However, even in the best of cases, there
were from one to two abnormal fluctuations in the results of
models, which disappeared during repeated training in one
place of the time series and appeared in another. To remove
these fluctuations, Delphi expert valuation method was used
(Chang et al. 2000). Its essence was:
1. Several neural networks were created and studied for
each model according to Eq. (4). In our case, their op-
timal number was nine. Their increase did not improve
the result.
2. Predictive values were calculated on the test sets of data
using the cross-validation method for each of the net-
works. The result was a matrix of type:
Resi=⎡
⎢
⎣
f1
i1··· f1
im
.
.
.....
.
.
f9
i1··· f9
im
⎤
⎥
⎦,(7)
where mis the size of the training sample for a particular
vector of the goals, the upper index is the serial number of
the neural network.
3. Each column was sorted and then 10% of records with
minimum and maximum values were removed from the
records.
4. For the remaining values for each of the columns, the
median was determined, which was considered to be the
result.
As a result of this phase, unlike linear models, for each of
the target vectors a list of nine trained neural networks was
received: Ti={Fn
i(X, Li,Ω
ANN
i,n )}n=1−9. The total num-
ber of neural networks was: 6 ·9·11 =594, considering
that for each cross-validation, 10 neural networks +1 net-
work were constructed and studied on the complete training
sample (necessary for further sensitivity analysis). To reduce
the computer time, parallel calculations were also used (the
same as at the cross-validation level).
7 Forecasting using recurrent neural
networks
One of the disadvantages of the above-mentioned ap-
proaches is that they do not take into account the cumulative
effect of the input field’s behavior during the studied lag.
That is, they take into account only one value of the input
factors shifted to a certain time interval. However, a situa-
tion may arise where the behavior of only one factor over
a certain period can lead to a crisis event. As noted above,
linear models and back propagation neural networks cannot
be used for this, as the number of input parameters will sig-
nificantly increase. The solution to this situation is the use
of recurrent neural networks (Greff et al. 2017). Feedback
connections are implemented in which the output signal is
fed to the input layer as additional inputs in order to take
into account the time behavior of the fields in the system.
Thus, the output signal depends on the previous state of the
system. Iteratively scrolling the signal, you can consider the
behavior of the system for a certain number of lagging steps.
In addition to this, it should be kept in mind that source
factors depend not only on the above-mentioned 5 input fac-
tors. This is a complex nonlinear system, which depends on
many factors not considered in the task. It is necessary to
add as input factors the value of the output factor at previous
moments to take into account their complex effect. To ac-
complish this the data set must be transformed into a three-
dimensional form in the following way:
Xi
L=X1(t −1),...,X
5(t −1), Ti(t −1),
X1(t −tL),...,X
5(t −tL), Ti(t −tL)>
(8)
Xi
3D,L =X1(t −l)l=1,L ,...,X
5(t −l)l=1,L,
Ti(t −l)l=1,L(9)
where tis row index, Lis maximum lag value, and iis target
index (2).
Output fields remain unchanged. Thus, we can see that
the number of input fields has increased by 1 due to adding
the output field. Each input represents an array of field val-
ues for a previous time lag L. Such a transformation of the
data set allows us to eliminate the dimensional problems and
take into account the behavior of input parameters over the
previous period. On the other hand, it is necessary to take
into account the previous values of the target factor. This

Space weather and hurricanes Irma, Jose and Katia Page 9 of 15 154
means that the number of rows in the data set will be re-
duced by the number of studied lags L. This, with a limited
size of data set, significantly reduces the size of the inves-
tigated lag L. That is why that it is impossible to take into
account lag =22 for LSTM recurrent Neural networks in
this case. The time interval L=4 hours was chosen for in-
vestigation.
A recurrent neural network with long short-term memory
(LSTM) was selected as an investigation model. This neu-
ral network allows you to simulate the behavior of a system
that depends on time delay. This is realized by reverse trans-
mission of the neural network output signal at the time t−1
back to the input of one of the network layers. This complex
input is used to calculate the output for time t.
LSTM is a type of the recurrent neural network, that al-
lows memorizing values for long or short periods. This net-
work does not use activation functions within its recurrent
components. Thus, the stored value does not disappear iter-
atively over time.
The LSTM blocks contain three or four “valves” that they
use to control the information flow to or from their memory.
These valves are used as logistic function to calculate val-
ues between 0 and 1. This value multiplies the allowance or
denial a partial flow of information to or from that memory
(Greff et al. 2017).
LSTM represents themselves a neural network that is
why the final value was calculated analogously to the clas-
sical neural network by the Delphi method.
8 Parallel calculations results of artificial
neural networks and linear models
The best way to describe how modeled data fit the real data
is to plot them on the single graph for each hurricane that has
been the subject of this study. The results of calculations for
linear models and artificial neural networks are presented in
Fig. 4.
As can be seen from Fig. 4, in the majority of cases,
LSTM models show the best prediction result for all six tar-
get vectors under study. Assigned before, only 4 hours lag
was used in calculations in LSTM RNN. This means that
the behavior of input factors at previous moments plays a
key role in hurricane forecasting. The results for artificial
neural networks and linear models are similar for the Irma
and Jose hurricanes (i.e. wind speed). As can be seen from
Figs. 4d–4f neural networks show significantly worse results
than LSTM and linear models. In the case of the Katia hur-
ricane, the lag of the optimal model for the RadioFlux field,
which is four and zero, is also strange. This is completely in-
consistent with the previous analysis. This can be explained
by the small dataset size (15 records) and, accordingly, the
inability of adequate training for both linear and neural net-
works. Regarding the Irma and Jose hurricanes, the obtained
lags are in good agreement with the previous analysis for the
RadioFlux field, which is the most influential (as it has been
shown above). A quantitative comparison of the accuracy of
results is presented in Table 5.
As can be seen from the table, the biggest determination
coefficient is observed for the LSTM models in all predic-
tions. The cross-validation testing confirmed that these mod-
els are accurate and adequate in the event of the hurricane
Irma. The small cross-validation coefficient for Jose can be
explained by the small lags that were taken into account in
LSTM models. The bad results for the Katia test can be ex-
plained by too small data set that lead to overfitting of the
LSTM model. In booth case (Irma and Katia) we need to
use more data to use LSTM models. That is mean that these
models are not adequate for this booth hurricanes.
Table 5shows that the highest determination coefficients
are obtained for target vectors such as the wind speed of
the Irma hurricane, the pressure of the Irma hurricane, and
wind speed of the Jose hurricane. Determination coefficients
for linear models and neural networks coincide. Cross-
validation results are slightly lower, but they also have high
values. This also confirms the adequacy of these models.
The table also demonstrates that pressure of the Jose hur-
ricane has low values of determination coefficients for both
the linear models and for neural networks. Therefore, the ac-
curacy of this model is low. Regarding the Katia hurricane,
it should be noted that similarly to the graphs, the results
are accurate for linear models and low for neural networks,
which may be caused by the small amount of the training
sample and overfitting on models.
During the calculations, the following optimal linear
models were obtained:
F1X, L1,ΩLin
1=−16.44 −1.09 ·x(3)1
+2.88 ·10−04 ·x(13)2−0.05 ·x(11)3
+0.85 ·x(2)4+1.40 ·x(7)5,(10)
F2X, L2,ΩLin
2=1067.52 +0.55 ·x(2)1
−5.42 ·10−04 ·x(2)2+0.02 ·x(12)3
+0.63 ·x(11)4−1.17 ·x(10)5,(11)
F3X, L3,ΩLin
3=−80.15 −0.71 ·x(4)1
+4.93 ·10−04 ·x(19)2+0.12 ·x(3)3
+1.62 ·x(14)4+0.84 ·x(18)5,(12)
F4X, L2,ΩLin
2=1073.42 +0.54 ·x(5)1
−2.83 ·10−04 ·x(2)2−0.08 ·x(4)3
−1.27 ·x(11)4−0.52 ·x(19)5,(13)
F5X, L5,ΩLin
5=−413.61 −94.62 ·x(2)1
−8.08 ·10−04 ·x(6)2

154 Page 10 of 15 Y. Vyklyuk et al.
Fig. 4 Results of hurricane forecasting with linear models and arti-
ficial neural networks for: (a) Wind speed of the Irma hurricane, (b)
Pressure of the Irma hurricane, (c) Wind speed of the Jose hurricane,
(d) Pressure of the Jose hurricane, (e) Wind speed of the Katia hurri-
cane, (f) Pressure of the Katia hurricane
+0.17 ·x(0)3−1.88 ·x(4)4
+3.14 ·x(4)5,(14)
F6X, L6,ΩLin
6=783.42 −26.24 ·x(5)1
+1.42 ·10−04 ·x(2)2
+0.12 ·x(3)3−2.30 ·x(1)4
+1.19 ·x(0)5,(15)

Space weather and hurricanes Irma, Jose and Katia Page 11 of 15 154
Table 5 Lags and determination coefficients of obtained models
Hurricane Parameter Model Numbers of
tests models
Lags R2Full
dataset
R2Cross
validation
Equation Type
Irma Wind speed F1(X, L1,Ω
Lin
1)Linear 1,048,576 L1=(3,13,11,2,7)0.89 0.85
{F1(X, L1,Ω
ANN
1)}ANN 99 0.89 0.75
{F1(X3D,L,L
LSTM,Ω
LSTM
1)}LSTM 99 LLSTM ={li=1,4}_i=1,6 0.98 0.88
Pressure F2(X, L2,Ω
Lin
2)Linear 759,375 L2=(2,2,12,11,10)0.90 0.88
{F2(X, L2,Ω
ANN
2)}ANN 99 0.90 0.87
{F2(X3D,L,L
LSTM,Ω
LSTM
1)}LSTM 99 LLSTM ={li=1,4}_i=1,6 0.99 0.93
Jose Wind speed F3(X, L4,Ω
Lin
4)Linear 5,153,632 L3=(4,19,3,14,18)0.86 0.77
{F3(X, L4,Ω
ANN
4)}ANN 99 0.86 0.74
{F3(X3D,L,L
LSTM,Ω
LSTM
1)}LSTM 99 LLSTM ={li=1,4}_i=1,6 0.98 0.61
Pressure F4(X, L4,Ω
Lin
4)Linear 5,153,632 L4=(5,2,4,11,19)0.69 0.56
{F4(X, L4,Ω
ANN
4)}ANN 99 0.58 0.70
{F4(X3D,L,L
LSTM,Ω
LSTM
1)}LSTM 99 LLSTM ={li=1,4}_i=1,6 0.98 0.45
Katia Wind speed F5(X, L5,Ω
Lin
5)Linear 100,000 L5=(2,6,0,4,4)0.98 0.96
{F5(X, L5,Ω
ANN
5)}ANN 99 0.72 0.34
{F5(X3D,L,L
LSTM,Ω
LSTM
1)}LSTM 99 LLSTM ={li=1,4}_i=1,6 0.95 0.48
Pressure F6(X, L6,Ω
Lin
6)Linear 59,049 L6=(5,2,3,1,0)0.98 0.96
{F6(X, L6,Ω
ANN
6)}ANN 99 0.65 0.53
{F5(X3D,L,L
LSTM,Ω
LSTM
1)}LSTM 99 LLSTM ={li=1,4}_i=1,6 0.99 0.38
Total Linear 12,274,264
ANN 594
LSTM 594
where the value of the lag is specified in the brackets of the
input parameters.
The result of the training neural networks is represented
by 54 neural networks whose parameters change during the
training, so it is not expedient to bring several dynamic ma-
trices of neurons’ weight factors.
The total number of tested linear models on account of
the proposed algorithm using decreased from 424,798,638
to 12,274,264 ·11 =135,016,904, i.e. the total number of
models is reduced to 32% of the previous indicator.
The using of neural networks within such an algorithm
takes several orders more time and requires, accordingly, the
involvement of a computer cluster.
9 Sensitivity analyses
To verify the adequacy of the models an analysis of the
model’s sensitivity to the change of factors for all models
in Table 5was performed (Pianosi et al. 2016). The analy-
sis was as follows. For each tuple rof the input parameters
vector Xr={xr
j}j=1−5
r=1−N
, (for LSTM models xr
jis a vector
of values during the lag L) which consists of Nrecords,
the input parameters value was incremented by 10% and
the change of the corresponding model Fi=1−6or the set
of models was calculated by the Delphi method (in the case
of neural networks). Then all the obtained values were av-
eraged. The resulting value represents the average change in
wind speed or pressure of the particular hurricane with an
increase of the input parameter by 10%.
To implement this, a diagonal matrix of variation factors
was created with a dimension equal to the number of input
parameters, in our case, five:
V=⎡
⎢
⎣
0.1··· 0
.
.
.....
.
.
0··· 0.1
⎤
⎥
⎦5×5
.(16)
Each tuple of the input parameters vector is duplicated
vertically in the amount which equals the length of the tuple
(that is, the number of input parameters):
Ar=⎡
⎢
⎣
xr
1··· xr
5
.
.
.....
.
.
xr
1··· xr
5
⎤
⎥
⎦.(17)

154 Page 12 of 15 Y. Vyklyuk et al.
The matrix of test values was calculated as an elemental
product of matrices:
Tr=(V +1)·Ar=⎡
⎢
⎣
1.1·xr
1··· 1.0·xr
5
.
.
.....
.
.
1.0·xr
1··· 1.1·xr
5
⎤
⎥
⎦.(18)
The vector of values was calculated:
Sr
i=FiTr,L
i,ΩLin(ANN)
i=⎡
⎢
⎣
fr
i,x1
.
.
.
fr
i,x5
⎤
⎥
⎦.(19)
An array of obtained changes of functions Fiis formed
by estimating the values Sr
ifor all tuples of vector X:
Si=⎡
⎢
⎣
(S1
i)T
.
.
.
(SN
i)T
⎤
⎥
⎦.(20)
Then the vector values predicted by the model was cal-
culated and duplicated horizontally by the amount of input
fields:
Mi=mr
ir=1−N=FiX, Li,ΩLin(ANN)
i,(21)
Mxi=⎡
⎢
⎣
m1
i··· m1
i
.
.
.....
.
.
mN
i··· mN
i
⎤
⎥
⎦N×5
.(22)
The last step was building a matrix of relative changes
by calculating the elemental difference and dividing the ma-
trices Mxiand Si. Then averaging by the columns is per-
formed:
D=(Si−Mxi)/Mxi,(23)
Sens =Dcol.(24)
The results of the calculations are given in Table 6.
As can be seen from the table, we got different results be-
tween the LSTM models and Linear with ANN. It can easily
be explained by a different approach by taking into account
the time lag behavior of input factors. Also, a different time
lag was used for these models. Therefore sensitivity analysis
should be done separately for these models.
As was shown before, the best models were obtained for
the Irma hurricane by the LSTM models. The sensitivity
analysis shows that the increasing Density during 4 hours
by 10% will lead to increasing of the wind speed by 40%.
Increasing of factors like P >100, E >2.0 and Speed will
decrease the wind speed. Also, this calculation shows that
Sun’s activity weakly impacts on pressure.
The most sensitive factor for Jose is F10.7. Increasing
this factor by 10% will lead to increasing speed by 123%
and decreasing pressure by 45%. These big numbers can be
explained by not good adequacy of the LSTM model for
this hurricane. A similar situation is observed for the Katia
hurricanes.
For the Linear and ANN models, as can be seen from
Table 6, the factor that has the greatest impact on the wind
speed of the hurricanes is F10.7. Its increase by 10% leads to
an increase in the wind speed for the Irma hurricane on av-
erage by 13%–14% in 42 hours (lag 7) and 11% in 4.5 days
(lag 18) for Jose. As the table shows, indicators of linear
models and neural networks are sufficiently close for all fac-
tors and these hurricanes, which confirm the adequacy of
the models. The second important indicator is the speed of
SW. Its increase by 10% raises the hurricane Jose’s speed by
9% after 18 hours (lag 3) and decreases the hurricane Irma’s
speed by 2.5% after 3 days. Other factors do not affect these
two hurricanes.
For the Katia hurricane, the sensitivity of wind speed on
F10.7 is 74% for the linear models and only 3% for neu-
ral networks. A strong difference in the sensitivity of neural
network and linear models also calls into question their ade-
quacy. This may be caused by a small amount of data, which
prevented the construction of an adequate model.
As known, the root cause of the wind is the pressure drop,
so it is interesting to analyze the influence of the SW pa-
rameters on air pressure. If we analyze the sensitivity of the
pressure for the Irma and Jose hurricanes, we can see that
they are less sensitive to changes in SW. In particular, chang-
ing the F10.7 by 10% causes a pressure drop of 1.3% after
2.5 days for the Irma hurricane and practically does not af-
fect the pressure of the hurricane Jose. However, as can be
seen from Fig. 2, the indicated parameter has increased from
August 28 to September 4, 2017, from 82.4 to 140, that is,
by 70%. According to Table 6, the change in only one of
these factors had to cause a pressure change in the hurricane
zone at 0.7/0.1(−1.3%)=−9.5%, that is, from 1004 mb to
908 mb. The actual recorded pressure was 914 mb (forecast
error is 0.6%). For the hurricane Jose, the calculated change
is 971 mb, the recorded is 938 mb (forecast error is 3.5%).
Thus, despite the low sensitivity of pressure on change of
the parameters of SW, strong fluctuations of the input pa-
rameters can cause a sharp decrease in pressure, and hence
the emergence of hurricanes.
10 Conclusions
Considering the potential prognostic models, one should
certainly bear in mind that for solar flares from active re-
gions located at the east heliolongitude, the time delay (be-
tween emission and the ground level enhancement onset)
can be from several hours up to days. Almost all diffusion

Space weather and hurricanes Irma, Jose and Katia Page 13 of 15 154
Table 6 Sensitivity analysis of the obtained models
Hurricane Parameter Model P >100 E >2.0 Speed Density F10.7
Irma Wind speed Linear −0.63% 0.10% −2.51% 0.23% 14.38%
ANN −0.65% 0.13% −2.64% 0.18% 13.05%
LSTM −12.76% −8.94% −28.36% 40.35% 0.46%
Pressure Linear 0.02% −0.04% 0.09% 0.02% −1.36%
ANN 0.02% −0.04% 0.09% 0.02% −1.36%
LSTM 0.15% −0.99% −1.77% −0.64% 0.20%
Jose Wind speed Linear −0.26% 0.50% 9.27% 0.64% 11.27%
ANN −0.26% 0.50% 9.27% 0.64% 11.27%
LSTM −0.03% −18.31% 1.89% −4.21% 123.51%
Pressure Linear 0.01% −0.04% −0.42% −0.04% −0.53%
ANN 0.00% 0.59% 3.63% 0.43% 5.24%
LSTM −0.02% −0.43% −6.93% 3.99% −44.84%
Katia Wind speed Linear −1.07% −1.19% 17.69% −1.17% 74.57%
ANN 0.00% −1.30% 8.80% −0.64% 3.33%
LSTM 4.77% 24.89% 547.95% 207.05% 0.80%
Pressure Linear −0.02% 0.05% 0.66% −0.07% 1.46%
ANN 0.00% −0.14% 2.65% 0.50% 6.98%
LSTM −3.33% 1.47% 7.15% −9.92% −8.46%
models involving solar particle transport in the interplane-
tary medium show that the maximum time delay is propor-
tional to the square of the distance traveled (Augusto et al.
2013).
The efficiency of the penetration depends on the degree
to which the interplanetary magnetic field provides input of
the particle flux to the region with the given angle, and/or
the percentage relation the particles of the given direction
are present in the flux with high angular isotropy.
Two different approaches were tested to take into account
the time delays between the parameters of solar activity and
the main characteristics of the hurricanes in this research.
In the first approach, a set of linear models with all possi-
ble lags of input parameters was investigated. The best of
the models were refined using be artificial neural networks.
The second approach was to use recurrent neural networks
LSTM. The time series of SW was chosen as input param-
eters for the training and testing. This makes it possible to
take into account the influence of the dynamics of changes
in input parameters on the characteristics of hurricanes. The
last approach has made it possible to describe and impart the
best of hurricane dynamics.
Research in this paper has shown that the applied model
is accurate and adequate to predict the appearance of hurri-
canes 2–4 days ahead, after the outbreak of SW. High deter-
mination coefficients sustain the previous conclusion. The
model can explain about 90% of variations of the Irma hur-
ricane. Jose is the hurricane in the Pacific Ocean, which has
a larger scale, and therefore the processes of the influence
of external factors are more inertial, which explains a bigger
lag in the calculations. The sensitivity analysis revealed that
F10.7 has the greatest impact on the hurricane wind speed,
except for the case of the Katia hurricane. In the general pic-
ture of the change in pressure and wind speed over a longer
period, the other factors were not taken into account in the
model. Therefore, the model for Jose was less accurate but
quite adequate. As already has been noted in Sect. 8,theKa-
tia hurricane was the least lengthy and the data were not suf-
ficient to test the hypothesis in this case. In all cases, LSTM
models showed the best results. But for effective use, big
data sets should be obtained.
Nikoli´
cetal.(2010), at the same time, explained that
charged particles can be associated with the origin of cy-
clonic airmass moving, which doesn’t always have to be rep-
resented exclusively by the hurricanes. Radovanovi´
cetal.
(2013) faced similar observations in the case of tornadoes
in Serbia. Gomes et al. (2012), among other things, consid-
ered a physical mechanism, which could explain a possible
connection. According to these authors, the appearance of
hurricanes Katrina, Rita, and Wilma are directly dependent
on the appropriate re-emergence of energy regions in the sun
in geoeffective position.
We can assume that the above results Vyklyuk et al.
(2017a), Vyklyuk et al. (2017b), and the results obtained in
this study are connected with the nature of the data used by
the ACE satellites. Namely, the position of this satellite is

154 Page 14 of 15 Y. Vyklyuk et al.
always located between the sun and the earth and that in
the relative time it measures the changes in the solar wind
parameter that is directed towards the Earth. This means
that after passing, for example, a particular energy region
through a geo-effective position, the ACE satellite no longer
detects the flow of high-energy particles. It is possible that
this connection could not be registered because the inter-
planetary magnetic field is moving in the form of curved
lines. Therefore, we consider that the continuation of the re-
search should be directed towards obtaining and processing
data on the parameters of the solar wind, which are directed
to our planet, which can be measured by other satellites.
Acknowledgements All original data used in this paper are publicly
available. The wind speed and the central pressure data of the Irma,
Jose and Katia hurricanes were downloaded from the Unisys archive
of hurricanes data. The Data Service Base of the Space Weather Pre-
diction Center (SWPC) was the source of solar particles and electron
flux data, while data on proton speed and proton density were obtained
from data archive of the SOHO CELIAS Proton Monitor. This paper is
a result of the project “Geografija Srbije” (No. III47007) funded by the
Ministry of Education, Science and Technological Development of the
Republic of Serbia.
Publisher’s Note Springer Nature remains neutral with regard to ju-
risdictional claims in published maps and institutional affiliations.
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