=Paper=
{{Paper
|id=Vol-2406/paper12
|storemode=property
|title=The Analysis of Current Neural Network
Configuration Used to Predict the Critical Frequency foF2 of the
Ionosphere
|pdfUrl=https://ceur-ws.org/Vol-2406/paper12.pdf
|volume=Vol-2406
|authors=Boris Salimov,Alexei Hmelnov,Oleg Berngardt
}}
==The Analysis of Current Neural Network
Configuration Used to Predict the Critical Frequency foF2 of the
Ionosphere==
https://ceur-ws.org/Vol-2406/paper12.pdf
The Analysis of Current Neural Network
Configuration Used to Predict the Critical
Frequency foF2 of the Ionosphere?
Boris Salimov1 , Aleksei Hmelnov2 , and Oleg Berngardt1
1
Institute of Solar-Terrestrial Physics of Siberian Branch of Russian Academy of
Sciences, Irkutsk, Russia
2
Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of
Russian Academy of Sciences, Irkutsk, Russia
Abstract. Ionosphere is the ionized part of the upper atmosphere con-
taining free electrons and ions. The critical frequency (foF2) is one of the
most important parameters of the ionospheric electron density, which af-
fects the functionality of radio communication and navigation equipment.
This frequency is a very variable parameter, which depends on various
geophysical parameters. Therefore, improving the accuracy of predicting
the critical frequency foF2 of the ionosphere is of great importance for
the proper operation of radio communication and navigation equipment.
Various physical and empirical models are used to predict this parame-
ter. The large amount of observational data and development of modern
machine learning algorithms make it possible to use new approaches for
predicting ionospheric parameters. In the paper we analyzed a neural
network created for predicting foF2 measured by Irkutsk Digisonde, as a
function of various geophysical parameters. We studied the contribution
of these parameters to the predicted foF2 frequency. It was shown that
the critical frequency of foF2 most strongly depends on 10.7 cm solar
radiation and on the local solar time.
1 Introduction
The characteristics of the ionosphere are of significant practical importance for
radio communications. Prediction of these characteristics allows one to work
more reliably with radio communication and navigation equipment. Many meth-
ods have been developed for predicting the ionospheric characteristics [1]. These
methods can be divided into techniques based on physical models and techniques
based on empirical models. One of the novel widely studied methods is the use of
machine learning for building empirical models. The method is mathematically
formulated as the detection of hidden patterns in numerical series and the con-
struction of approximation schemes based on these patterns. The large amount of
?
The work was performed with budgetary funding of Basic Research program II.12.
The results were obtained using the equipment of Center for Common Use “Angara”
http://ckp-rf.ru/ckp/3056.
available measurement data and the growth of computational capabilities allow
one to use very complex empirical prediction models - artificial neural networks.
One of the key ionospheric parameters is the foF2 frequency. The critical
frequency foF2 is the maximal frequency of a radio wave propagating vertically
and reflecting from the ionosphere [2]. If the frequency of the radio wave exceeds
the critical frequency the wave penetrates the ionosphere. The foF2 critical fre-
quency is frequently used for predicting the radio wave propagation character-
istics. So the knowledge of this frequency is of practical importance for radio
communications.
The foF2 dependence on the indices of solar and geomagnetic activity is
well known [3]. The dependence of foF2 on the solar radiation intensity at the
wavelength of 10.7 cm is especially significant. The physical reason of such a
dependence is an increase in atmospheric ionization with an increase in solar
radiation intensity, which can be detected by an increase in solar radio emission
flux. The dependence of foF2 on the geomagnetic activity (for example on ap-
index) is also known. In this paper, we use Dst, ap and Kp geomagnetic activity
indices for predicting foF2. The planetary index Kp describes the geomagnetic
disturbance in the three-hour interval. The initial data for the calculation of the
Kp index is the K-index data of the twelve observatories located between 63 °
and 48 ° north and south of the geomagnetic latitudes. The K-index takes values
from 0 to 9, where 0 corresponds to undisturbed conditions and 9 corresponds
to a very strong geomagnetic disturbance [4].
The index ap is calculated from the Kp-index data. It represents the change
in the most disturbed geomagnetic field component D or H over the 3-hour
time interval at mid-latitude stations and is calculated in units of 2γ. The ap
index is refered as the planetary amplitude in the 3-hour interval. The Dst-
index characterizes the intensity of the symmetric ring current, which is typically
observed in the recovery phase of a geomagnetic storm. Dst-index is the average
value of the geomagnetic disturbance over the hourly interval, calculated over
the network of low-latitude geomagnetic stations separated by longitude. The
unit of measurement for the Dst-index is γ. To calculate the Dst-index, the data
from 4 geomagnetic stations are used [4].
For analysis we use measurements of the foF2 critical frequency near Irkutsk,
made with the DPS-4 digisonde from 2009 to 2016. The DPS-4 digisonde has
two 150W transmitters, four receiving antennas and a “crossed vertical rhombs”
transmitting antenna system. The digitization module has the ability to simul-
taneously register in the automatic mode the following radio signal parameters:
amplitude, frequency, height (range), angles of arrival, phase, polarization, and
Doppler frequency shift of the radio waves reflected by the ionosphere [5]. Ob-
servations of the digisonde are obtained from the ISTP database [6]. Solar and
geomagnetic indices for the same period are obtained from publically available
databases (OMNI database [7]).
2 Model development and input data
To take into account the periodicity of foF2 changes, in addition to the solar and
geomagnetic indices mentioned above, a periodic function is used that depends
on the day number in a year. The periodic functions that depend on the hour of
the day have also been used.
2π · DOY
cosDOY (LST ) = cos (1)
365.25
2π · HOD
cosHOD(LST ) = cos (2)
24
2π · HOD
sinHOD(LST ) = sin (3)
24
where HOD is the ordinal hour number of the day (from 0 to 23, we use local
solar time), DOY is the ordinal day number of the year (from 1 to 365 or 366).
We train our foF2 prediction algorithms based on the following dataset:
cos DOY (LST), cos HOD (LST) and sin HOD (LST), f10.7 solar index, Dst,
Kp, ap geomagnetic indicies, foF2.
The resulting dataset is divided into two subsets: the training dataset and
the test dataset in a ratio of 80 to 20%, respectively. The whole experimental
data set consists of 61675 elements.
An artificial neural network is a collection of interconnected perceptrons (neu-
rons) aggregated into layers. Each perceptron in the neural network converts its
input to its output by making a linear combination of input values and using it
as an argument for some (’activation’) function:
OutN (w, x) = σ(w1 · x1 + w2 · x2 + w3 · x3 + . . . + wn · xn + b) (4)
where {xi |x2, x3, x4, x5 , . . . , xn } - is a set of input attributes, wi , b - weights, and
σ(x) is an activation function.
For prediction of foF2 we trained a neural network with two hidden layers
with 11 and 5 neurons in each, and a sigmoid activation function. The model
was built on the basis of the Python scikit-learn software library and the Percep-
tron Multi-layer class [8], with “adam” solution algorithm, and a regularization
coefficient of 0.001. We used an algorithm with back propagation of an error for
training the neural network [9].
3 Discussion
An example of the forecast over test dataset is shown in Figure 1. The prediction
over test dataset provides a Pearson correlation coefficient of 0.89, a root mean
square error of 0.84MHz and a mean absolute percent error of 14.7%. A high
correlation coefficient and a rather small root-mean-square error indicate that
the model is of sufficient quality to predict the ionospheric critical frequency.
Fig. 1. Neural network forecast values compared with experimental data
To estimate the degree of influence of various input parameters on the final
result we made an analysis of the weights inside each neuron.
Table 1. The weights in the neurons of the first layer of the neural network
Neuron Kp index Dst-index(nT) ap index(nT) f10.7 index cos HOD(LST) sin HOD(LST) cos DOY(LST) ABS SUM
10 -0,054 -0,336 -0,083 0,088 -5,389 3,258 -2,847 12,055
11 0,069 -0,197 -0,049 0,324 -3,618 -1,991 -4,058 10,306
1 0,795 -0,106 -0,761 0,012 0,244 -2,911 -4,56 9,389
6 0,118 -0,21 -0,346 4,781 -1,968 0,669 -0,473 8,565
2 0,181 0,248 -0,027 -0,202 -3,496 -1,388 -2,874 8,416
9 -0,137 0,344 -0,23 -0,094 -2,171 3,1 -0,552 6,628
7 0,269 -0,022 -0,385 2,149 -0,01 -0,875 -2,329 6,039
3 0,286 -0,233 -0,142 -0,201 -3,436 -0,814 0,035 5,147
8 -0,026 -0,255 0,094 3,333 0,335 0,534 -0,282 4,859
4 0,131 -0,301 -0,137 -0,304 -0,737 0,426 -1,534 3,57
5 0,03 0,048 0,086 -0,305 0,774 0,607 -1,546 3,396
Table 1, 2, and 3 show the weights values inside each neuron in the first layer
(see Table 1), second layer (see Table 2) and output layer (see Table 3). The
last column of the Table 1 and Table 2 corresponds to the sum of the absolute
values of the weight coefficients in each neuron. The rows of the table are sorted
in descending order by this parameter, allowing us to find the neurons of higher
importance.
As one can see from Table 1, the first three most influential neurons (marked
by color) of the first layer have significant prevalence of weights corresponding to
Table 2. The weights in the neurons of the second layer of the neural network
Neuron Neuron out 1 Neuron out 2 Neuron out 3 Neuron out 4 Neuron out 5 Neuron out 6 Neuron out 7 Neuron out 8 Neuron out 9 Neuron out 10 Neuron out 11 ABS SUM
3 -1,522 1,016 -2,01 1,172 -4,614 1,944 1,508 1,437 1,493 -5,129 -3,106 26,558
4 -0,091 2,578 -0,416 -4,699 -3,057 2,292 -2,229 1,704 1,265 0,086 -0,098 19,906
2 0,173 -0,813 1,675 -1,246 3,007 2,07 4,023 -0,308 -1,337 1,815 0,556 16,917
5 0,069 2,653 0,942 -3,453 -0,784 -0,18 -0,639 2,541 1,847 0,511 0,376 18,013
1 0,75 -0,249 1,704 -3,85 0,529 -0,176 1,492 1,883 -0,402 -0,148 1,905 18,612
Table 3. Output layer of the neural network
Neuron Neuron out 1 Neuron out 2 Neuron out 3 Neuron out 4 Neuron out 5
1 2,09 1,941 -3,122 3,378 4,599
local time and date (cos HOD (LST), sin HOD (LST), cos DOY (LST)), showing
the importance of regular daily and seasonal variations in foF2 dynamics.
As one can see from Table 2 the first most influential neuron (marked by
color) of the second layer contains large coefficients (-5.139 and 3.106) at the
outputs of the tenth and eleventh neurons of the first layer (which are the most
influential in the first layer). At the same time, the coefficients at the output of
the sixth, seven and eighth neurons of the first layer are also significant (1.944,
1.508 and 1.437). These neurons of the first layer have the greatest weights
corresponding to the index f10.7 (solar radiation flux at a wavelength of 10.7
cm).
The output layer (see Table 3) has coefficients of approximately the same
order. This allows us to ignore the output neuron and to limit the analysis of
the most influential neurons to analysis of the first two layers. From this we can
conclude that the main contribution to the neural network output is produced
by solar radiation index f10.7 and solar local time and date.
4 Conclusion
In this paper we described our experience in creating and training a neural net-
work for predicting the critical frequency foF2 using data obtained at Irkutsk
with the DPS4 Digisonde for the period 2009-2016, as well as solar and geomag-
netic indices for the same period. It is shown that average model accuracy is
about 0.84MHz and Pearson correlation coefficient is 0.89.
We analyzed the structure of the network and showed that variations in the
ionospheric critical frequency foF2 are mostly caused by f10.7 index and period-
ical daily and seasonal variations. The dependence of foF2 on the geomagnetic
indices Dst, ap, and Kp is much weaker. This result corresponds well with phys-
ical mechanisms of formation F2 layer in the ionosphere and can be explained
by an increase in the ionospheric ionization intensity with the solar radiation
intensification and the daily and seasonal dynamics of the solar zenith angle.
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