Canoer 719_724

719

ANNALS OF GEOPHYSICS, VOL. 46, N. 4, August 2003

Ionospheric storm forecasting technique
by artifi cial neural network

Ljiljana R. Cander (1), Milan M. Milosavljević (2) and Saša Tomasević (2)
(1) Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, U.K.

(2) Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia and Montenegro

Abstract
In this work we further refi ne and improve the neural network based ionospheric characteristic’s foF2 predictor,
which is actually a neural network autoregressive model with additional input signals (NNARX). Our analysis
is focused on choice of X parts of NNARX model in order to capture middle and long term dependencies. Daily
distribution of prediction error suggests need for structural changes of the neural network model, as well as
adaptation of running average lengths used for determination of X inputs. Generalisation properties of proposed
neural predictor are improved by carefully designed pruning procedure with additional regularisation term in
criterion function. Some results from the NNARX model are presented to illustrate the feasibility of using such
a model as ionospheric storm forecasting technique.

Mailing address: Dr. Ljiljana R. Cander, Rutherford
Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX,
U.K.; e-mail: l.cander@rl.ac.uk

Key words prediction and forecasting – neural
networks – ionospheric storms modelling – space
weather

1. Introduction

There are a number of methods available
for prediction and forecasting characteristics
relevant to ionospheric telecommunication ap-
plications (Kutiev et al., 1999; Fuller-Rowell
et al., 2000; Muhtarov et al., 2001; Muhtarov
et al., 2002; Cander, 2003 and references therein).
The user usually requires ionospheric forecasting
that are near real time for radar and surveillance
applications and over 1-24 h ahead for point-
to-point and mobile communications (Cander,
1998). The neural network non-linear techniques
are based on finding more complex correla-
tion over a greater number of steps. Successful

attempts to build different artifi cial neural net-
works models for the critical frequency of
the ionospheric F2 layer, foF2, prediction and
forecasting have already been made at monthly
(Lamming and Cander, 1998, 1999) and daily time
scales (Williscroft and Poole, 1996; Altinay et al.,
1997; Wintoft and Cander, 2000a,b; Francis et
al., 2001).

The aim of the paper is to provide a concise
summary of the application and development of
non-linear neural network techniques to improve
ionospheric storm forecasting capabilities. It is
shown that the NNARX - neural network based
autoregressive model with additional inputs (X)
can provide forecasting of the hourly variation
of foF2 from 1 h ahead, as the shortest time scale
over which the ionosphere can be predicted
forwards extremely well.

2. foF2 data source

The data used for foF2 forecasting 1 h ahead
are values taken from the Rutherford Appleton
Laboratory CD-ROM produced within COST
251 project (http://www-cost251.rcru.rl.ac.uk/)

720

Ljiljana R. Cander, Milan M. Milosavljević and Saša Tomasević

for a few European stations listed in table I. The
forecast periods were chosen to be February 1986,
September and December 1990 representing low
and high solar activity as well as geomagnetically
disturbed and quiet periods. Table II gives the
details concerning the solar-terrestrial conditions
during selected periods.

The NNARX model was trained using hourly
foF2 values from 01 January to 31 December
during years of 1986 and 1990 excluding months
for which forecasting has been made: February
in case of 1986, September in case I on 1990 and
December in case II on 1990.

In table II R
i
is the international relative

sunspot number and A
p
is an averaged planetary

geomagnetic index based on data from a set of
specifi c geomagnetic observatories. It serves to
classifi ed the storms as follows:

1) Minor geomagnetic storm: a storm for
which the A

p
index was greater than 29 and less

than 50.
2) Major geomagnetic storm: a storm for

which the A
p
index was greater than 49 and less

than 100.
3) Severe geomagnetic storm: a storm for

which the A
p
index was 100 or more.

The D
st
index is an index of geomagnetic

activity derived from a network of near-equatorial
geomagnetic observatories that measures the
intensity of the globally symmetrical equatorial
electrojet (the «ring current»). Peaks Dst values
are between – 20 and 20 nT during quiet geo-
magnetic condition and decrease to below – 100
nT during highly disturbed periods. In the case
of severe geomagnetic storms, Dst values are
below – 250 nT.

3. NNARX model and training procedure

NNARX - neural network based auto-
regressive model with additional inputs (X) is
one possible approach that use the hybrid time-
delay multi-layer percepton neural network with
only critical frequency of the ionospheric F2 layer
as input parameter to produce one output foF2
value at hour t + 1. Inputs (X) include foF2 value
at time t, seven days mean MfoF2 values and

Ionospheric
stations

URSI
codes

Latitude
(N)

Longitude
(E)

Rome RO041 41.9 12.5

Sofi a SQ143 42.7 23.4

Grocka BE145 44.8 20.5

Poitiers PT046 46.6 0.3

Slough SL051 51.5 – 0.6

Julisruh JR055 54.6 13.4

Moscow MO155 55.5 37.3

Uppsala UP158 59.8 17.6

Table I. List of European ionospheric stations with
their URSI codes and geographical coordinates.

Months Days with storm
commencement

Min D
st

geomagnetic index
Max A

geomagnetic index

February 1986 with
monthly mean sunspot
number R

i
= 23.2

06 at 1312 UT – 307 nT on 9 February 208 on 8 February

September 1990 with
monthly mean sunspot
number R

i
= 125.2

01 at 1024 UT – 48 nT on 1 September 26 on 1 September

December 1990 with
monthly mean sunspot
number R

i
= 129.7

21 at 1724 UT – 47 on 24 December 15 on 24 December

Table II. Solar-terrestrial conditions during selected periods used in this study.

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Ionospheric storm forecasting technique by artifi cial neural network

4. NNARX model results

Accuracy of prediction, clearly stating
range and scope of test conditions, i.e., show
the breakdown between training and test data,
indicate any comparisons made with other
or reference models such as persistence for
example. For comparative purposes the accuracy
of the NNARX model is quoted in terms of both
the Root Mean Square (RMS) error and the
Normalised RMS Error defi ned as

where x are the actual foF2 values, y are the
predicted foF2 values, n = S

i
is the total number

of comparisons between actual and predicted
values and s is the standard deviation of the
actual values from the mean value given by

The predictive accuracy of the NNARX model
is summarised in the tables III and IV. In these
tables all errors are quoted with respect to the
one step ahead NNARX predictive model, for
the entire test set in each instance. The per-
sistence model results are included in table III
as an effective reference in each instance. It
can be seen in these RMS and NRMS errors

appropriate differences DMfoF2 at particularly
selected hours (t, t – 1, t – 23, t – 47) as well
MfoF2 at forecast time (t + 1) calculated using
only the learning set of data to generate the
background daily variations of foF2. Detailed
description of this type of the neural network as
far as its architecture, fi rst and second hidden
layers, learning and test data sets are concerned
can be found in Cander et al. (1998a,b).

The NNARX is trained using cost function
with a weight-decay term (Bishop, 2000). Our
experimental experience showed that only the
weight-decay scheme is not enaugh to overcome
the overfi tting problem. Namely, it would have
been possible to increase the weight-decay
parameters, which have also been tried, but
when increasing the weight-decay parameters
the quadratic error term in the cost-function
increase. This is an undesirable effect, as it is
this part of the cost function that is especially
interesting and should be minimized as much as
possible. Therefore a pruning scheme is used to
remove superfl uous parameters from the network
architecture (Le Cun et al., 1990). The so called
Akaike’s Final Prediction Error (FPE) estimate of
the test error is used to point out which structure
is the optimal (Akaike, 1969). Additionally, we
then tried to retrain the optimal network structure
to see if it is possible to overcome the problem
of overtraining when optimal network structure
already has been found. The experimental results
showed that retrained optimal networks possess
very good generalyzation properties. All results
presented in sequal are obtained by the such
retrained optimal networks.

σ 2

=
−( )∑ X x

i
i .

Ionospheric stations RMS error (MHz) NRMSE

February 1986 Persistence NNARX model Persistence NNARX model

RO041 0.6482 0.4456 0.4740 0.3258

SQ143 0.6178 0.4460 0.4469 0.3226

PT046 0.8097 0.4745 0.3568 0.2091

SL051 0.7213 0.5258 0.5285 0.3853

MO155 0.6121 0.3778 0.4288 0.2647

Table III. RMS and NRMS errors at different stations for February 1986.

NRMSE = −( )











∑ x y ni i
i

2 2σ

722

Ljiljana R. Cander, Milan M. Milosavljević and Saša Tomasević

values that there is a substantial improvement
in NNARX model over persistence results for all
stations during severe geomagnetic conditions in
February 1986. Table IV gives only RMS errors
for NNARX model results in case of moderate
and quiet geomagnetic conditions in September
and December 1990. With the exception of the
Sofi a ionospheric station RMS errors, it is clear
that the NNARX model results are as good
as these in table III with a slight tendency of
becoming worse during the more or less quiet
geomagnetic activity in December 1990.

Encouraging results in tables III and IV
of comparisons between actual and 1 h ahead

Ionospheric
stations

RMS error (MHz)
NNARX model
September 1990

case I

RMS error (MHz)
NNARX model
December 1990

case II

RO041 0.49 0.57

SQ143 0.96 0.88

PT046 0.45 0.60

SL051 0.44 0.58

UP158 0.44 0.60

Table IV. RMS errors at different stations for Sep-
tember and December 1990.

Stations/NNARX model
input parameters

RO041
MAPE (%)

SQ143
MAPE

(%)

PT046
MAPE

(%)

SL051
MAPE

(%)

JR055
MAPE

(%)

MO155
MAPE

(%)

UP158
MAPE

(%)

foF2 only 8.86 10.22 9.14 8.94 10.66 8.95 9.42

foF2 + R
i
+ A

p
8.71 10.07 8.63 9.10 10.79 9.88 10.25

foF2 + R
i
+ D

st
8.93 9.86 8.89 9.18 10.19 9.59 10.29

foF2 + R
i
+ A

p
+ D

st
8.70 9.90 8.60 9.26 10.46 9.97 11.03

Table V. MAPE (%) at different ionospheric stations for February 1986.

Stations/NNARX model
input parameters

RO041
MAPE

(%)

SQ143
MAPE

(%)

BE145
MAPE

(%)

PT046
MAPE

(%)

SL051
MAPE

(%)

JR055
MAPE

(%)

UP158
MAPE

(%)

foF2 only 4.16 8.85 4.97 4.26 4.62 4.52 6.20

foF2 + R
i
+ A

p
4.04 8.88 4.98 4.23 4.60 5.05 6.27

foF2 + R
i
+ D

st
4.18 8.94 4.99 4.24 4.57 4.60 6.05

foF2 + R
i
+ A

p
+ D

st
4.07 8.82 4.99 4.30 4.57 4.79 6.08

Table VI. MAPE (%) at different European ionospheric stations for September 1990.

Stations/NNARX model
input parameters

RO041
MAPE

(%)

SQ143
MAPE

(%)

PT046
MAPE

(%)

BE145
MAPE

(%)

SL051
MAPE

(%)

JR055
MAPE

(%)

UP158
MAPE

(%)

foF2 only 7.05 11.41 6.48 7.62 6.82 8.23 11.53

foF2 + R
i
+ A

p
7.22 11.27 6.23 7.34 6.63 8.60 10.26

foF2 + R
i
+ D

st
7.13 11.65 6.32 7.40 6.82 8.81 10.61

foF2 + R
i
+ A

p
+ D

st
6.73 12.40 6.54 8.53 6.72 8.62 9.03

Table VII. MAPE (%) at different European ionospheric stations for December 1990.

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Ionospheric storm forecasting technique by artifi cial neural network

forecast foF2 values show that there is a
predictive advantage to neural network modelling
which make it a useful tool to be introduced into
the current ionospheric weather applications. For
these purposes, it is shown here an interesting
effect of different solar-terrestrial indices on 1 h
ahead foF2 forecasting by NNARX model. This
time the prediction accuracy has been examined
in terms of the Mean Absolute Percentage Error
(MAPE) defi ned as

A more in depth investigations of neural network
forecasting of the key ionospheric characteristic
foF2 at different European ionospheric stations
shown in tables V, VI and VII clearly demonstrate
that 1 h ahead forecasting performances are not
signifi cantly improved by adding solar activity R

and/or geomagnetic A
p
and D

st
indices as NNARX

input parameters. It should be emphasised that
these data and comparisons are specifi cally for
a few stations but the results are applicable to
the entire mid-latitude region at European longi-
tudinal domain.

5. Conclusions

A neural network method has been developed
for 1 h ahead forecasting of foF2. Comparisons
with observations are very encouraging because
of a very small errors and a high consistence be-
tween diurnal morphologies exhibited by fore-
casting method and observed trends. Further-
more, the effects of including various solar and
geomagnetic indices as input parameters to the
neural network were investigated, and it was
found that performance was not improved by
adding an index. Indeed, the NNARX model
does not require neither predicted nor past values

MAPE
abs

% .( ) =
−( )

⋅
=
∑

1
100

x y

x
i i

Fig. 1. Measured and NNARX model forecast foF2 values for a 8 day period in February 1986 at Slough
ionospheric station.

724

Ljiljana R. Cander, Milan M. Milosavljević and Saša Tomasević

of solar and geomagnetic indices to forecast 1 h
ahead foF2 values even during geomagnetically
very disturbed periods as those in February 1986
(see fi g. 1). It remains to be seen to what extent the
artifi cial neural network performance, such as the
NNARX model, can be improved in predicting
foF2 values up to 24-h ahead. NNARX model
is implemented in MATLAB 5.2.1 and requires
its installation on PC Pentium II platform. It has
MATLAB type of friendliness with low level of
interaction and requires training data for foF2
for recent 365 days.

This work could be extended to space weather
forecasting with the application of predicting
disturbance effects. This will clearly involve
prediction techniques based on the access and
manipulation of real time ionospheric data.

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(received May 2, 2003;
accepted July 10, 2003)