In this work we further refine 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

Cander, L. R.

Milosavljevic´, M. M.

Tomasevic´, S.

Earth-prints Repository

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. Milosavljevic´  (2) and Saša Tomasevic´  (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. Milosavljevic´  and Saša Tomasevic´
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 Ri is the international relative 
sunspot number and Ap 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 Ap index was greater than 29 and less 
than 50.
2)  Major geomagnetic storm: a storm for 
which the Ap index was greater than 49 and less 
than 100.
3)  Severe geomagnetic storm: a storm for 
which the Ap 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 Ap 
geomagnetic index
February 1986 with 
monthly mean sunspot 
number Ri = 23.2 
06 at 1312 UT – 307 nT on 9 February 208 on 8 February
September 1990 with 
monthly mean sunspot 
number Ri = 125.2
01 at 1024 UT – 48 nT on 1 September 26 on 1 September
December 1990 with 
monthly mean sunspot 
number Ri = 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.
721
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 = Si 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
2
=
−( )∑ X x
n
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 ii
2 2σ
722
Ljiljana R. Cander, Milan M. Milosavljevic´  and Saša Tomasevic´
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 + Ri + Ap 8.71 10.07 8.63 9.10 10.79 9.88 10.25
foF2 + Ri + Dst 8.93 9.86 8.89 9.18 10.19 9.59 10.29
foF2 + Ri + Ap + Dst 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 + Ri + Ap 4.04 8.88 4.98 4.23 4.60 5.05 6.27
foF2 + Ri + Dst 4.18 8.94 4.99 4.24 4.57 4.60 6.05
foF2 + Ri + Ap + Dst 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  + Ri + Ap 7.22 11.27 6.23 7.34 6.63 8.60 10.26
foF2  + Ri + Dst 7.13 11.65 6.32 7.40 6.82 8.81 10.61
foF2  + Ri + Ap + Dst 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.
723
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 Ri 
and/or geomagnetic Ap and Dst 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
1N
x y
x
i i
ii
N
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. Milosavljevic´  and Saša Tomasevic´
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. 
REFERENCES
ALTINAY, O., E. TULUNAY and Y. TULUNAY (1997): 
Forecasting of ionospheric frequency using neural 
networks, Geophys. Res. Let., 24, 1467-1470.
AKAIKE, H. (1969): Fitting autoregressive models for 
prediction, Ann. Inst. Stat. Mat., 21, 243-247.
BISHOP, C.M. (2000): Neural Networks for Pattern 
Recognition (Oxford University Press, Oxford), 
pp. 504.
CANDER, LJ.R. (1998): Space weather effects on tele-
communication, in AI Applications in Solar-Terrestrial 
Physics, edited by I. SANDAHL and E. JONSSON, 
ESA WPP-148 Proceedings, 35-42.
CANDER, LJ.R. (2003): Toward forecasting and mapping 
ionospheric space weather under the COST actions, 
Adv. Space Res., 31 (4), 957-964.
CANDER, LJ.R., S. STANKOVIC´  and M. MILOSAVLJEVIC´  
(1998a): Dynamic ionospheric prediction by neural 
networks, in AI Applications in Solar-Terrestrial Physics, 
edited by I. SANDAHL and E. JONSSON, ESA WPP-148 
Proceedings, 225-228.
CANDER, LJ.R., M.M. MILOSAVLJEVIC´ , S.S. STANKOVIC´  
and S. TOMASEVIC´ (1998b): Ionospheric forecasting 
technique by artifi cial neural network, Electron. Lett., 
34 (16), 1573-1574.
FRANCIS, N.M., A.G. BROWN and P.S. CANNON (2001): 
Predictionn of the hourly ionospheric parameter foF2 
using a novel nonlinear interpolation technique to cope 
with missing data points, J. Geophys. Res. Space Phys., 
106 (A12), 30,415-30,428. 
FULLER-ROWELL, T., E. ARAUJO-PRADERE and M. 
CONDRESCU (2000): An empirical ionospheric stort-time 
correction model, Adv. Space Res., 25 (1), 138-148.
LAMMING, X. and LJ.R. CANDER (1998): Monthly median 
ionospheric frequencies model using neural networks, in 
AI Applications in Solar-Terrestrial Physics, edited by I. 
SANDAHL and E. JONSSON, ESA WPP-148 Proceedings, 
229-234.
LAMMING, X. and LJ. R. CANDER (1999): Monthly median 
foF2 modelling COST251 area by neural networks, Phys. 
Chem. Earth (C), 24 (4), 349-354.
LE CUN, Y., J.S. DENKER and S.A. SOLLA (1990): Optimal 
brain demage, in Advances in Neural Information 
Processing Systems, edited by M. KAUFMAN, vol. 2, 
598-605 
MUHTAROV, P., I. KUTIEV, LJ.R. CANDER, B. ZOLESI, G. DE 
FRANCESCHI, M.F. LEVY and M. DICK (2001): European 
ionospheric forecasting and mapping, Phys. Chem. 
Earth (C), 26 (5), 347-351. 
MUHTAROV, P., I. KUTIEV and LJ.R. CANDER (2002): 
Geomagnetically correlated autoregression model for 
short-term prediction of ionospheric parameters, Inverse 
Problems, 18, 49-65.
KUTIEV, I., P. MUHTAROV, LJ. R. CANDER and M.F. LEVY 
(1999): Short-term prediction of ionospheric parameters 
based on auto-correlation analysis, Ann. Geofi s., 42 (1), 
121-127.
WILLISCROFT, L.-A. and A.W.A. POOLE (1996): Neural 
networks, foF2, sunspot number and magnetic activity, 
Geophys. Res. Lett., 23, 3659-3662.
WINTOFT, P. and LJ.R. CANDER (2000a): Twenty-four hour 
predictions of foF2 using time delay neural networks, 
Radio Sci., 35 (2), 395-408.
WINTOFT, P. and LJ.R. CANDER (2000b): Ionospheric foF2 
storm forecasting using neural networks, Phys. Chem. 
Earth (C), 25 (4), 267-273. 
(received May 2, 2003;
accepted July 10, 2003)
  


Ionospheric storm forecasting technique by artificial neural network

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Ionospheric storm forecasting technique by artificial neural network

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