=Paper= {{Paper |id=Vol-2540/article_11 |storemode=property |title=Input parameter ranking for neural networks in a space weather regression problem |pdfUrl=https://ceur-ws.org/Vol-2540/FAIR2019_paper_50.pdf |volume=Vol-2540 |authors=Stefan Lotz,Jacques P. Beukes,Marelie H. Davel |dblpUrl=https://dblp.org/rec/conf/fair2/LotzBD19 }} ==Input parameter ranking for neural networks in a space weather regression problem== https://ceur-ws.org/Vol-2540/FAIR2019_paper_50.pdf

Input parameter ranking for neural networks in
a space weather regression problem

Stefan Lotz1,2[0000−0002−1037−348X] , Jacques P. Beukes2,3[0000−0002−6302−382X] ,
and Marelie H. Davel2,3[0000−0003−3103−5858]
1
South African National Space Agency (SANSA), Space Science directorate,
Hermanus, slotz@sansa.org.za
2
Multilingual Speech Technologies, North-West University, South Africa
3
Centre for Artiﬁcial Intelligence Research (CAIR), South Africa.
marelie.davel@nwu.ac.za, jpbeukes27@gmail.com

Abstract. Geomagnetic storms are multi-day events characterised by
signiﬁcant perturbations to the magnetic ﬁeld of the Earth, driven by so-
lar activity. Numerous eﬀorts have been undertaken to utilise in-situ mea-
surements of the solar wind plasma to predict perturbations to the geo-
magnetic ﬁeld measured on the ground. Typically, solar wind measure-
ments are used as input parameters to a regression problem tasked with
predicting a perturbation index such as the 1-minute cadence symmetric-
H (Sym-H) index. We re-visit this problem, with two important twists:
(i) An adapted feedforward neural network topology is designed to en-
able the pairwise analysis of input parameter weights. This enables the
ranking of input parameters in terms of importance to output accu-
racy, without the need to train numerous models. (ii) Geomagnetic storm
phase information is incorporated as model inputs and shown to increase
performance. This is motivated by the fact that diﬀerent physical phe-
nomena are at play during diﬀerent phases of a geomagnetic storm.

Keywords: Space weather · Input parameter selection · Neural network

1 Introduction

Violent eruptions of electromagnetic energy (solar ﬂares) and charged plasma
(coronal mass ejections or CMEs) on the solar surface are propagated through
interplanetary space and can impact the Earth’s geomagnetic ﬁeld. These per-
turbations can result in the disruption of various kinds of technological systems:
satellite [2] and HF radio communications [5] are aﬀected by the increased energy
and particle density in the atmosphere and near Earth space; electrical faults
can develop on space craft due to anomalous charging [1]; and power grids, oil
pipelines and ground-based telecommunication are aﬀected by low frequency
currents induced by the changing geomagnetic ﬁeld [3,16]. Due to the adverse
eﬀects that damage to critical technological infrastructure can have on modern
society, major eﬀorts are being made to eﬀectively monitor and predict space
weather and its impact on speciﬁc technologies [14,13].
2 S. Lotz et al.

The intervals of geomagnetic activity that routinely causes the most intense
disturbances are known as geomagnetic storms [6] – prolonged periods of sig-
niﬁcant perturbation to the geomagnetic ﬁeld usually driven by CMEs. The in-
tensity of geomagnetic storms are quantiﬁed by the net disturbance to the ﬁeld,
measured on Earth by any of the dedicated geomagnetic observatories found
on all six continents [8]. There are several indices derived from magnetic ﬁeld
measurements to quantify certain aspects of the disturbances. In this work we
use the symmetric H index (Sym-H, described in Section 2).
To understand the drivers of geomagnetic disturbances (GMD), characteristic
parameters of the solar wind plasma and magnetic ﬁeld are analyzed. These are
measured upstream of the Earth by several satellites [20,19] that orbit the ﬁrst
Lagrangian point (L1) about 1.5 million kilometres upstream of the Earth. Solar
wind propagation speed near 1 astronomical unit (≈ 1.5 × 108 km; the distance
from sun to Earth) range from about 300 km/s (quiet periods) to over 1,000
km/s (severely disturbed), and yields a natural lead time for predictions ranging
from about 20 to 90 minutes. Therefore the prediction of some terrestrial index
of GMD from measurements taken in the solar wind naturally lends itself to
modelling as a regression problem, and as such many attempts have been made
to provide forecasts of a variety of disturbance indices tailored to speciﬁc space
weather eﬀects [15,17,11,7].
Figure 1 shows the progression of a geomagnetic storm over about four days.
The top panel shows the Sym-H index and the lower two panels show solar
wind parameters measured by the Advanced Composition Explorer (ACE) space-
craft [20]. This storm was due to a single CME impacting the magnetosphere.
The passage of ejecta past the spacecraft is recognisable as the increase in density
and speed, and the ﬂuctuations in the interplanetary magnetic ﬁeld (IMF).
A typical geomagnetic storm is seen in the Sym-H curve, starting with the
onset phase with the arrival of the CME on 17 March, then moving in to the main
phase as the IMF turns southward (BZ < 0). Southward IMF enables enhanced
coupling between the solar wind and magnetospheric plasma, resulting in more
eﬃcient energy transfer from the solar wind to the geomagnetic ﬁeld. After the
IMF turns northward (BZ > 0) and the bulk of the disturbed solar wind plasma
has passed, the magnetosphere can recover (the recovery phase of the storm).
The objective of the solar wind–Sym-H regression model is to use solar wind
parameters to predict Sym-H, while taking advantage of the natural lead time
aﬀorded by the distance between the space craft and the magnetosphere. In
this work, we have an additional goal: to determine whether an analysis of the
network can shed light on the physical processes being modelled. We use the solar
wind - Sym-H regression problem as test case because the mechanisms of the
solar wind - magnetosphere coupling is fairly well understood, and therefore it
is known which solar wind parameters are predominantly responsible for driving
GMD on the ground. This however, is not the case for more complex problems in
space physics and other ﬁelds, so this paper serves as an initial proof of concept,
before other more complex problems will be tackled in future.
Input parameter selection for space weather regression NN 3

Fig. 1. A typical geomagnetic storm driven by a single CME. The top panel shows
Sym-H, with the horizontal green line indicating the -100 nT level. The entire event
from start to end is used to develop the model, as is the case for the other 96 storms
identiﬁed between 2000 – 2018. The lower panels show solar wind parameters Vsw ,
Np , and BZ , BT respectively. The shaded area indicates the main storm phase. The
intervals before and after the main phase are identiﬁed as the onset and recovery phases,
respectively.

With this in mind, we revisit the regression problem (where we task a feed-
forward neural network to predict Sym-H from solar wind parameters) with two
important changes: Firstly, an adapted network topology is designed to enable
the pairwise analysis of input parameter weights. Consider the problem of hav-
ing access to data from m input parameters (x1 , x2 , . . . , xm ) that are used to
estimate y through some transfer function F:

y ≈ F(x1 , x2 , . . . , xm ) (1)

There are various ways of pruning Equation 1 so that those inputs that do not
add any value to the model are removed, but these require separate models such
as random forests or exhaustive iterations through the possible combinations of
inputs [9]. In this work a novel FFNN topology is introduced. The “pairwise”
network has input nodes paired up in their connections to the hidden layer (see
Section 4.1). This enables input parameter pairs to be ranked during model
development, thus reducing user interaction overhead and development time.
The second change is the use of storm phase information as an additional
input to the model. It is known that diﬀerent physical phenomena are at play
during diﬀerent phases of a geomagnetic storm. We show that simply including
4 S. Lotz et al.

phase information in the set of input parameters improves prediction perfor-
mance. Finally we show how the input parameter rankings change when re-
stricting the model to only one storm phase, further demonstrating the utility
of analysing parameter importance to gain insight into the problem at hand,
beyond merely seeking accurate predictions.

2 Input and output parameters

Before we introduce the data set itself, we describe the physical quantities used
as input to the task, as well as the construction of the Sym-H index.

2.1 Solar Wind Parameters

Solar wind data is collected from the High Resolution OMNI data set [18]. Mea-
surements taken at 16 or 64 second cadence (depending on the instrument) are
averaged to 1-minute values and shifted in time to the estimated position of
the magnetospheric bow shock nose (BSN) [18]. This ensures that the propa-
gation time from L1 to the BSN does not have to be incorporated into model
development. Several plasma and magnetic ﬁeld parameters are included in this
study, all contributing to some extent to the dynamics involved in driving a
geomagnetic storm:

Vsw Solar wind speed [km/s] is the bulk speed of the plasma moving across the
spacecraft.
Np Proton number density [#/cc] measured in particles per cubic centimetre
indicates the particle density of the plasma. Coronal mass ejecta are usually
more dense than the ambient solar wind plasma.
Pd Dynamic ﬂow pressure [nPa] is the ﬂow pressure of the solar wind and is
2
linearly related to Np Vsw .
EM Merging electric ﬁeld in the solar wind [mV/m] serves as an indication of
the coupling between the solar wind and magnetospheric plasmas and is
linearly related to −Vsw BZ .
BX,Y,Z , BT The three components of the IMF, measured in nT, and the total
ﬁeld BT .

2.2 Sym-H index

The target or output parameter to the regression problem is the Sym-H index.
This is an index calculated at 1-minute cadence, derived from the horizontal
(with regard to the Earth’s surface) component of the geomagnetic ﬁeld mea-
sured at 11 middle latitude magnetic observatories. Sym-H serves as an indica-
tion of the strength of the ring current [12] which circles the Earth and is the
main driver of magnetic storm activity on the ground.
Input parameter selection for space weather regression NN 5

3 Data sets
The data set consists of solar wind and Sym-H data, at 1-minute cadence, from
the period 2000 – 2018. This period includes almost two full solar activity cycles
and is therefore representative of a wide range of geomagnetic storms in terms
of drivers and intensity.

3.1 Event selection
Geomagnetic storms are fairly rare events and as such only intense geomagnetic
storms, those with minimum Sym-H < −100 nT, were selected out of the 19
year period. Using all available data would result in a very unbalanced data set,
with the storm periods being under-represented. The event selection algorithm is
described in [10]. Using this method 97 storms are identiﬁed, resulting in 396,164
minutes of data (excluding missing values) out of a possible ∼ 9.9 × 106 minutes.
The collection of distinct storms are used to divide the data in to training (67
storms), testing (15 storms) and validation (15 storms) sets. Keeping storm
intervals separate ensures that the three sets are truly independent – every storm
interval is wholly contained in only one of the three data sets. The training set is
used during training to adapt weights through the backpropagation algorithm,
the validation set is used to determine the model’s performance after each epoch,
and the test set serves as the independent out of sample data set on which the
model’s performance is ultimately calculated. The entire data set is standardized
by removing the mean and scaling to unit variance.
Within each storm, the onset, main and recovery phases are identiﬁed by
searching for the (i) interval around the positive increase in Sym-H (onset phase),
(ii) the rapid decrease to storm minimum (main phase), and ﬁnally the (iii)
recovery period from the minimum Sym-H until the end of the event. These
identiﬁers are important because there are diﬀerent physical processes involved
in the various storm phases.

4 Model development
Two diﬀerent types of architectures are utilised, a standard fully-connected
FFNN and a “pairwise” neural network, detailed below (Section 4.1). The same
process is utilised to optimize all networks, as described in Section 4.2.

4.1 The Pairwise net
A fully-connected feedforward network layout mixes signal from all inputs as
information ﬂows through the hidden layers to the output. This enables the
training procedure to utilise all the diﬀerent combinations of input parameters to
ﬁnd an eﬃcient solution. Analysis of these sets of combinations are prohibitively
complicated since from the ﬁrst layer of hidden nodes, every node is directly
or indirectly connected to every input parameter. Selectively removing some
6 S. Lotz et al.

connections from the input layer to the ﬁrst hidden layer results in distinct
combinations of inputs to be fed to the subsequent hidden layers of a network.
In this work we introduce the “pairwise” network, constructed by the follow-
ing procedure. Given a model with M input parameters, H hidden nodes in a
single hidden layer, and K output nodes:

1. Find all possible distinct pairs of inputs {Xi , Xj } (i �= j) in the list {X1 , X2 , . . . , XN }.
Say there are P such pairs, and note that {Xi , Xj } ≡ {Xj , Xi }.
2. Divide the set of hidden nodes in to P distinct groups.
3. Fully connect each pair of inputs to its corresponding group of hidden nodes.
4. Fully connect all the hidden nodes to the output nodes.

The pairwise net is described with an example problem where Np , Vsw and BT
are used to estimate Pd . Figure 2(a) shows the layout, with connections coloured
by input parameter to aid the visualisation.
Input parameter ranking is performed by tracking the sum of normalised
weights at every training epoch for the pairs of inputs in the pairwise network.
The idea behind this method follows naturally from how neural networks are
trained. During back-propagation, weights are updated according to their gra-
dient, i.e. their inﬂuence on the loss value. Weights that improve the loss are
ampliﬁed and weights that worsen the loss value are attenuated. With this in
mind, the combination of weights in the ﬁnal layer of the pairwise model be-
comes a measure of the preceding sub-network’s importance to the output value
of this regression problem. Weights are ﬁrst normalized across the network to
ensure that the values of weights in the last layer can be compared. Similar to
[4], we calculate the norm of the fan-in weight vector at each node and divide
the fan-in weights and multiply the fan-out weights with this value. This has
no eﬀect on the function the network represents but ensures that the weight
values are comparable per layer. In practice, the sum of weights are averaged
over several seeds.
In this example we know the pair (Vsw , Np ) should yield the highest sum of
2
weights, since Pd ∼ Np Vsw , and the pairs that include the less useful input BT
are suppressed by the training algorithm. This is indeed what happens, according
to the weights plotted in Figure 2(b): the sum of weights dominate for pair (Vsw ,
Np ), while the other two pairs are suppressed.

4.2 Parameters and procedure of model development

Two distinct network layouts are investigated in this work: feedforward networks
and the pairwise net layout described above. The baseline model (hereafter la-
belled B1 ) is a fully connected FFNN with solar wind parameters as input and
Sym-H as output. Model B1 is trained with the 8 solar wind inputs, two hidden
layers of 10 nodes each and a single output node (Sym-H).
Since diﬀerent physical processes are at play during the three storm phases,
categorical input parameters are created to indicate phase. The relevant phase
indicator is set to 1 when the appropriate phase (onset, main or recovery) is in
Input parameter selection for space weather regression NN 7

(a) Pairwise network layout. The (b) Weight evolution over 10 epochs of
double-headed arrows indicate full con- training.
nection (for picture clarity).

Fig. 2. Pairwise network with three inputs and one output. Dynamic pressure Pd is
predicted by three parameters, BT , Vsw and Np , while it is known that only two of
them are useful (Vsw and Np ).

progress, and set to 0 at other times. Therefore, model B2 has 8 + 3 = 11 input
parameters.
A further improvement is made by adding temporally shifted versions of each
parameter to the set of inputs. For each input parameter Xt , measured at time
t, another input Xt−m is added, doubling the number of inputs of model B3
to 16. The magnetosphere has a measure of “memory” in that the magneto-
hydrodynamic processes that govern the storm time phenomena take some time
to react and recover from solar wind energy input [12]. In this case we let m = 270
minutes, chosen by a parametric search of shifts. Applying this time shift resulted
in a marked increase in performance (see Section 5).
Various pairwise network models are developed. A simple model with the 8
solar wind inputs and 10 hidden nodes in 2 hidden layers is trained (P1 ), and
is shown to perform as well as model B1 . This shows that the pairwise nodes
do not reduce performance for this application. Subsequent pairwise models are
developed by adding phase and time-shifted parameters (P2 and P3 ).
Both the Bi and Pi models are trained with Adam as the optimizer and
mean squared error as the loss function. Correlation between the predicted and
observed output is used as a performance metric. All optimization decisions are
based on the model’s performance on the validation set. Early stopping is im-
plemented by selecting models with the largest validation correlation. Extensive
probing showed that weight decay, batch normalization and learning rate sched-
ulers make little to no improvement to the performance, therefore none of these
are used. It was also found that smaller mini-batches have better performance,
so a mini-batch size of 64 is chosen. Increasing the network width or depth does
not improve performance, therefore the mentioned network sizes are chosen as
such in favour of computational eﬃciency. A grid search is done to determine
the best learning rate. Three initialization seeds are considered for both the Bi
8 S. Lotz et al.

and the Pi models. The test results of these models are listed in Table 1 and
discussed in the next section.

5 Results
5.1 Baseline model
Without phase or time-shifted inputs, the optimal baseline model (B1 ) has a
0.63 test correlation. By adding phase (B2 ) or time-shifted inputs (B3 ), the
performance increases to 0.79 and 0.76, respectively. With both phase and time-
shifted inputs added (B4 ), the model reaches a test correlation of 0.83.
Figure 3 shows an example of Sym-H predicted by models B1 and B4 during
a geomagnetic storm. It clearly shows the advantage of adding phase information
and time-shifted parameters to the set of inputs, especially during the onset and
recovery phases.

Table 1. Model performance for the diﬀerent model types.

Model Description Layout Test Corr. S.E.
B1 FFNN 8:(10,10):1 0.63 0.0008
B2 FFNN with phase (8+3):(10,10):1 0.79 0.0081
B3 FFNN with time-shifted inputs (8+8):(10,10):1 0.76 0.0100
B4 FFNN with phase and t-shifted inputs (8+3+8+3):(10,10):1 0.83 0.0047
P1 Pairwise net 8:(10,10)a :1 0.66 0.0066
P2 Pairwise net with phase (8+3):(10,10)a :1 0.81 0.0022
P3 Pairwise net with time-shifted inputs (8+8):(10,10)a :1 0.77 0.0022
P4 Pairwise net with phase and t-shift (8+3+8+3):(10,10)a :1 0.81 0.0056
a
Hidden layers of the pairwise model’s sub-networks

5.2 Pairwise net
With no phase information or time-shifted inputs (P1 ), the best model has a 0.66
correlation on the test set. By adding phase (P2 ) or time-shifted (P3 ) inputs, the
validation correlation increases to 0.81 and 0.77, respectively. With both phase
and time-shifted (P4 ) inputs, the test correlation is 0.81.

5.3 Input parameter ranking through pairwise net
The pairwise net P1 is developed with (i) the entire data set, and (ii) with the
dataset divided according to the three storm phases. This enables the ranking of
input pairs in general and for separate storm phases. This is to see if the input
ranking via the pairwise nets reﬂects the known diﬀerences in physical phenom-
ena at play during the diﬀerent storm phases. In both cases the best performing
Input parameter selection for space weather regression NN 9

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Fig. 3. Predicted and observed Sym-H values during a geomagnetic storm. Model pre-
diction results are shown both with and without phase and time-shifted inputs. The
diﬀerent storm phases are also indicated here.

pairwise model is used. Ranking is done by taking the sum of absolute normalized
weights on the epoch where the model achieved its best validation performance.
The results are then averaged over 4 iterations with diﬀerent initialization seeds.
All 8 input parameters are considered in pairs of 2. Table 2 shows the resulting
average sum S of absolute normalized weights after the last epoch, for the top
ranked and bottom ranked input pairs.

6 Discussion and Conclusions

6.1 Model performance

This investigation conﬁrms that neural networks are a viable option for predict-
ing a geomagnetic storm index (i.e. Sym-H) only from solar wind parameters.
The simplest model are able to reach a test correlation of 0.63. By adding phase
and temporal information, the performance increases to 0.83.
The proposed pairwise network achieved approximately the same predictive
performance as the simple baseline neural network, with the added beneﬁt of
ranking the importance of input parameters.

6.2 Interpretation of the input parameter selection

The pairwise nets enable a crude form of input parameter ranking, built in to
the framework of a fully connected FFNN, without the need for explicit ranking
procedures. The sum of absolute normalized weights S at the ﬁnal epoch is listed
10 S. Lotz et al.

in Table 2. It shows the top-ranked and bottom-ranked input pairs for all phases
and is then separated by phase.
The ﬁrst pair of columns in Table 2 lists the input pairs arranged by S for
the entire data set (i.e. all storm phases). The remaining three pairs of columns
lists inputs pairs with their respective S for each storm phase.
For entire storms the most inﬂuential pair of inputs is (Vsw , EM ). Both of
these parameters serve as general indicators of geoeﬀective solar wind activity.
Geomagnetic storms are broadly characterised by sudden increase and subse-
quent gradual decrease in solar wind speed, and EM is a proxy for the energy
input in to the magnetosphere, as it is related to BZ and Vsw . Most of the
top-ranked pairs are physically relevant as they are all related to the typical
processes involved in geomagnetic storms, such as increased dynamic pressure
and solar wind forcing (Vsw , Pd and Np ), and reconnection (BZ and EM ).
The second pair of columns shows the ranking for onset phase. Top ranked
are the pairs (BT , BZ ) and (BT , EM ) – both of these pairs indicating general
increase in activity around onset and the reconnection (indicated by negative
BZ ) necessary for storm onset. The lowest ranked pairs are dominated by BX
and BY which are not very inﬂuential in storm development.
For the storm main phases EM and Vsw dominate top ranked pairs. The
inclusion of BX in the top pair is slightly puzzling, as according to current
understanding of main phase dynamics, it should not play a big role. The bottom
ranked pairs include parameters such as density (Np ) with BX and BY .
During storm recovery it is the absence of input from the solar wind that
allows the magnetosphere to recover by various wave-particle interactions that
allow energetic particle populations to lose energy. Here the top ranking pair
of inputs is (BT , Vsw ) – both of these parameters serve as general indicators
of disturbances in the solar wind. After a CME passes the solar wind speed
gradually decreases to ambient level and the ﬂuctuations in the IMF decrease
signiﬁcantly. Both of these are indicators of the solar wind plasma and magnetic
ﬁeld returning to an ambient state.

All Onset Main Recovery
Rank Pair S Pair S Pair S Pair S
28 BY , EM 0.567 BX , BY 0.241 BY , Np 0.206 BX , Pd 0.363
27 BX , BY 0.601 Pd , EM 0.274 BX , Np 0.242 BY , Pd 0.423
26 Np , EM 0.622 BY , EM 0.303 BY , Pd 0.246 Np , Pd 0.432
25 BX , Np 0.630 BX , Pd 0.333 BX , Pd 0.265 Pd , EM 0.433
1 Vsw , EM 1.369 BT , BZ 0.755 BX , EM 0.578 BT , Vsw 0.931
2 BT , Vsw 1.125 BT , EM 0.752 Vsw , EM 0.547 Vsw , Pd 0.808
3 BY , Pd 1.112 Vsw , EM 0.680 BZ , Pd 0.537 BT , EM 0.795
4 BT , Pd 1.095 Vsw , Pd 0.648 BT , Vsw 0.523 BT , Np 0.769
Table 2. Sum of weights S for the top ranked (1–4) and bottom ranked (25–28) pairs
of inputs, for training set consisting of all data and separated by storm phase.
Input parameter selection for space weather regression NN 11

6.3 Conclusions and further work
In this work we illustrated how domain knowledge can increase the performance
of a neural network based model on a well-known regression problem and that
smart model design can inform domain knowledge. In this age of rapidly in-
creasing machine learning capability researchers and domain experts need to be
cognisant of the dangers of well performing, but un-explainable models.
Revisiting the well-known solar wind–Sym-H regression problem, we showed
that adding storm phase and time-shifted solar wind parameters increases model
performance, as would be expected given the current understanding of the prob-
lem. Then, a novel neural network layout was introduced that allows an, admit-
tedly crude, way of ranking the available set of input parameters. It was shown
that (i) the modiﬁcations does not decrease performance when compared to a
simple FFNN and that (ii) the rankings, calculated by taking the sum of nor-
malised weights, generally agrees with the current understanding of the problem.
Further development of the pairwise network introduced here will concentrate
on a more rigorous analysis and interpretation of weight analysis during training,
and eventually the application of these ideas to more complex problems.

References
1. Baker, D.N.: The occurrence of operational anomalies in spacecraft and their rela-
tionship to space weather. IEEE Transactions on Plasma Science, 28(6), pp.2007-
2016 (2000).
2. Béniguel, Y. and Hamel, P.: A global ionosphere scintillation propagation model
for equatorial regions. Journal of Space Weather and Space Climate, 1(1), p.A04
(2011).
3. DH Boteler: Assessment of Geomagnetic Hazard to Power Systems in Canada,
Natural Hazards, Vol 23, pg. 101 – 120 (2001).
4. Davel, M.: Activation gap generators in neural networks, South African Forum for
Artiﬁcial Intelligence Research (FAIR 2019), submitted for publication.
5. Frissell, N. A., Vega, J. S., Markowitz, E., Gerrard, A. J., Engelke, W. D., Erickson,
P. J., et al.: High-frequency communications response to solar activity in September
2017 as observed by amateur radio networks. Space Weather, 17, 118–132 (2019).
DOI: 10.1029/2018SW002008
6. Gonzalez, W. D., Joselyn, J. A., Kamide, Y., Kroehl, H. W., Rostoker, G., Tsu-
rutani, B. T., & Vasyliunas, V. M.: What is a geomagnetic storm? Journal of
Geophysical Research, 99(A4), 5771 (1994). DOI: 10.1029/93JA02867
7. Gruet, M. A., Chandorkar, M., Sicard, A., & Camporeale, E.: Multiple-hour-
ahead forecast of the Dst indexusing a combination of long short-termmemory
neural network and Gaussianprocess. Space Weather,16, 1882–1896 (2018). DOI:
10.1029/2018SW001898
8. Intermagnet Homepage, http://www.intermagnet.org. Last accessed 10 Oct 2019.
9. Lotz, S. I., Heyns, M. J., and Cilliers, P. J.: Regression-based forecast model of
induced geo-electric ﬁeld. Space Weather, 15, 2016. ISSN 1542-7390. http://dx.
doi.org/10.1002/2016SW001518.
10. Lotz, S. I., and Danskin, D. W.: Extreme value analysis of induced geoelectric ﬁeld
in South Africa. Space Weather, 15. doi: 10.1002/2017SW001662 (2017).
12 S. Lotz et al.

11. Lotz, S., Heilig, B., and Sutcliﬀe, P.: A solar-wind-driven empirical model of Pc3
wave activity at a mid-latitude location. Annales Geophysicae, 33, 225–234, 2015.
DOI:10.5194/angeo-33-225-2015.
12. Moldwin, M.: An Introduction to Space Weather, Cambridge University Press
(2008).
13. Oughton, E. J., Hapgood, M., Richardson, G. S., Beggan, D., Thomson, A. W.
P., Gibbs, M., Horne, R. B. (2018). A Risk Assessment Framework for the Socioe-
conomic Impacts of Electricity Transmission Infrastructure Failure Due to Space
Weather: An Application to the United Kingdom. Risk Analysis, (November).
https://doi.org/10.1111/risa.13229
14. Pecasus, http://pecasus.eu/. Last accessed 10 Oct 2019.
15. Siscoe, G., McPherron, R. L., Liemohn, M. W., Ridley, A. J., & Lu, G.: Reconciling
prediction algorithms for Dst. Journal of Geophysical Research: Space Physics,
110(December 2004), 1–8. DOI: 10.1029/2004JA010465
16. Trichtchenko, L., & Boteler, D. H.: Modelling of geomagnetic induction in pipelines.
Annales Geophysicae, 20(7), 1063–1072 (2002). DOI: 10.5194/angeo-20-1063-2002
17. P Wintoft, Wik, M., Lundstedt, H., Eliasson, L.: Predictions of local ground ge-
omagnetic ﬁeld ﬂuctuations during the 7–10 November 2004 events studied with
solar wind driven models. Ann. Geophys. 23, 3095–3101 (2005).
18. OMNIWeb Homepage, https://omniweb.gsfc.nasa.gov/. Last accessed 10 Oct
2019.
19. DSCOVR Homepage, https://www.nesdis.noaa.gov/content/
dscovr-deep-space-climate-observatory. Last accessed 10 Oct 2019.
20. Advanced Composition Explorer, http://www.srl.caltech.edu/ACE/. Last ac-
cessed 10 Oct 2019.