The electric field amplitude of very low frequency (VLF) transmitter from Hawaii (NPM) has been continuously recorded at Chofu (CHF), Tokyo, Japan. The VLF amplitude variability indicates lower ionospheric perturbation in the D region (60–90 km altitude range) around the NPM-CHF propagation path. We carried out the prediction of daily nighttime mean VLF amplitude by using Nonlinear Autoregressive with Exogenous Input Neural Network (NARX NN). The NARX NN model, which was built based on the daily input variables of various physical parameters such as stratospheric temperature, total column ozone, cosmic rays, Dst, and Kp indices possess good accuracy during the model building. The fitted model was constructed within the training period from 1 January 2011 to 4 February 2013 by using three algorithms, namely, Bayesian Neural Network (BRANN), Levenberg Marquardt Neural Network (LMANN), and Scaled Conjugate Gradient (SCG). The LMANN has the largest Pearson correlation coefficient (r) of 0.94 and smallest root-mean-square error (RMSE) of 1.19 dB. The constructed models by using LMANN were applied to predict the VLF amplitude from 5 February 2013 to 31 December 2013. As a result the one step (1 day) ahead predicted nighttime VLF amplitude has the r of 0.93 and RMSE of 2.25 dB. We conclude that the model built according to the proposed methodology provides good predictions of the electric field amplitude of VLF waves for NPM-CHF (midlatitude) propagation path.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2016RS006022

One day prediction of nighttime VLF amplitudes using nonlinear autoregression and neural network modeling

The space between the two spherical conducting shells, Earth surface and the lower boundary of the ionosphere, behaves as a spherical cavity in which some electromagnetic signals can propagate a long distance and is called Earth-ionosphere waveguide. Through this waveguide ultra low frequency (ULF), extremely low frequency (ELF) and very low frequency (VLF) signals can propagate efficiently with low attenuation. Resonances which occur for ELF waves due to round-the-world propagation interfering with $2n \pi $
 phase difference are called Schumann resonances. Lightnings are the main sources of energy continuously producing these electromagnetic radiations from the troposphere. Some fixed frequency signals are also transmitted through the waveguide from different stations for navigation purposes. The intensity and phase of these signals at a particular position depend on the waveguide characteristics which are highly influenced by different natural events. Thus the signatures of different geophysical and extra-terrestrial events may be investigated by studying these signals through proper monitoring of the time series data using suitable techniques. In this article, we provide a review on ULF, ELF and VLF signals within the waveguide in terms of different geophysical and extra-terrestrial events like lightning, earthquakes, Leonid meteor shower, solar flares, solar eclipse, geomagnetic storms, and TLEs etc.

Studies on different geophysical and extra-terrestrial events within the Earth-ionosphere cavity in terms of ULF/ELF/VLF radio waves

The electromagnetic field amplitude of the subionospheric Very Low Frequency (VLF) propagation is sensitive to the lower ionospheric conditions. Accordingly, VLF waves have been proposed to study and monitor the lower ionosphere (D/E region). In this paper, the NARXNN (Nonlinear Autoregressive with Exogenous Input Neural Network) is used as a method for predicting the daily nighttime mean amplitude of VLF transmitter signals indicating the ionospheric perturbation around the transmitter-receiver path. The NARXNN has a good accuracy in predicting time series data and thus are more suitable for dynamic modeling. The NARX constructed model, which was built based on daily input variables of various physical parameters with the time interval from 1 January 2011 to 4 February 2013 such as stratospheric and mesospheric temperatures, cosmic rays, total column ozone, F10.7, Kp, AE, and Dst indices. We used the constructed model to predict high-(NLK-CHF), middle-(NPM-CHF) and low-latitude (NWC-CHF) paths. As a result, the constructed models are capable of performing reasonably good 5-day ahead predictions of the daily nighttime of VLF electric field amplitude for NPM-CHF path with the Pearson correlation coefficient (r) of 0.84 and with Root Mean Square Error (RMSE) of 3.12 dB, NLK-CHF (r = 0.80, RMSE = 3.57 dB) and NWC-CHF (r = 0.79, RMSE = 2.60 dB). We conclude that the constructed NARX NN model is capable of predicting the VLF electric field amplitude variation for different latitude paths.

Multi step ahead prediction of nighttime VLF amplitude signal for low-, mid-and high-latitude paths

A large part of the path of the Annular Solar Eclipse of May 20,2012 (magnitude 0.9439) (ASE-2012) was over southern Japan. The D-region ionospheric changes associated with the ASE-2012, led to several degree of observable perturbations of sub-ionospheric very low frequency (VLF) radio signal. The solar eclipse associated signal changes were identified in VLF several receiving stations $(R_{x})$ simultaneously for the VLF signals coming from both Japanese and US VLF transmitters ($T_{x}$). In this work, we have analyzed temporal dependences of VLF electric amplitude perturbation $(\Delta A_{ecl,obs}(t))$ from two Japanese VLF transmitters (JJI (22.2kHz) and JJY (40.0kHz)), and the spatio-temporal characteristics of respective subionospheric perturbations are studied in detail. We consider the 2-parameter D-region ionospheric model with the exponential electron density profile. To model the shadow effect on the D-region ionosphere due to obscuration of solar disk, we assume a generalized space-time dependent 2-Dimensional Elliptical Gaussian distribution Model (2DEGM) for ionospheric parameters, such as, effective reflection height $(h')$ and sharpness factor $(\beta )$. In the vicinity of the eclipse zone, we compute the subionospheric VLF signal propagation for several signal propagation paths. In the simulation, we obtain the perturbation of VLF signal amplitude ($\Delta A_{ecl,LWPC}(t))$ at each station and compare with its observtaional counterpart $(\Delta A_{ecl,obs}(t))$.

Modeling of VLF network observations due to lower ionospheric perturbation during a solar eclipse

Very low frequency (VLF) waves have been used as a powerful tool to monitor and study the lower ionosphere (D/E region). In this paper, nonlinear physical processes of VLF signals propagation can be well represented by nonlinear autoregressive with exogenous input neural network (NARXNN) model. Further, a study of NARXNN model to predict the daily nighttime mean amplitude of VLF propagation wave to recognize the ionospheric perturbation along the great circle path. The NARXNN model is powerful in predicting time series data and suitable representations of a variation of nonlinear models. The daily input variables of various physical parameters with the time interval from 15 March 2014 to 26 May 2016 were used to build prediction model. The results of the built models are performing reasonably good for one-step ahead (OSA) predictions of the daily nighttime of VLF electric field amplitude. The NARXNN model has good performance for predicting the VLF amplitude variation for different latitude paths.

Prediction of VLF Sub-Ionospheric Wave Propagation Using Nonlinear System Identification

The UEC's VLF/LF transmitter observation network has been operating years in order to monitor the ionospheric perturbations caused by various physical phenomena. A solar eclipse is one of the factors that produce disturbances in the lower ionosphere. In this paper, we analyze VLF amplitude data from our network associated with annular solar eclipse in 2012. Clear temporal dependences of the VLF/LF amplitude were identified at various VLF/LF receivers. Numerical computations of VLF/LF signals with the ionospheric perturbations due to the solar eclipse were carried out by using 2D-FDTD method. As a result, temporal variations of the VLF/LF amplitude are in rather good agreement with those from the numerical modeling.

Daiki Inui

Papers

Spatio-temporal characteristics of sub-ionospheric perturbations associated with annular solar eclipse over Japan: Network observations and modeling

Spatio-temporal characteristics of subionospheric perturbations associated with annular solar eclipse