Time constants in the ionosphere from neural network models

Neural network (NN) models for the low latitude and the polar ionosphere from the D- to the F-region were developed which are based on incoherent scatter radar data from Arecibo and EISCAT Svalbard, respectively. The various geophysical input parameters defining the NN are not only the ones that represent the time one wants to predict, but also the geophysical conditions prior to the time of the prediction. The optimum length of these preceding periods are derived for the two models are different, but a period of 60 days is a compromise acceptable for both latitudes. Furthermore from the Arecibo data time constants of electron density decay after sundown are derived which – arguably – are also relevant elsewhere, including the polar latitudes. Whereas at all altitudes the electron densities decay exponentially after sundown, below 300 km there is an additional variation with solar zenith angle.     

Computerized ionospheric tomography with the IRI model

Computerized ionospheric tomography (CIT) is a method to estimate ionospheric electron density distribution by using the global positioning system (GPS) signals recorded by the GPS receivers. Ionospheric electron density is a function of latitude, longitude, height and time. A general approach in CIT is to represent the ionosphere as a linear combination of basis functions. In this study, the model of the ionosphere is obtained from the IRI in latitude and height only. The goal is to determine the best representing basis function from the set of Squeezed Legendre polynomials, truncated Legendre polynomials, Haar Wavelets and singular value decomposition (SVD). The reconstruction algorithms used in this study can be listed as total least squares (TLS), regularized least squares, algebraic reconstruction technique (ART) and a hybrid algorithm where the reconstruction from the TLS algorithm is used as the initial estimate for the ART. The error performance of the reconstruction algorithms are compared with respect to the electron density generated by the IRI-2001 model. In the investigated scenario, the measurements are obtained from the IRI-2001 as the line integral of the electron density profiles, imitating the total electron content estimated from GPS measurements. It has been observed that the minimum error between the reconstructed and model ionospheres depends on both the reconstruction algorithm and the basis functions where the best results have been obtained for the basis functions from the model itself through SVD.     

Using neural networks to determine the optimum solar input for the prediction of ionospheric parameters

Neural networks (NNs) are proving to be ideal tools for modeling the behaviour of the ionosphere. The NNs are trained using a database of archived data describing the relationship between the output parameter and an input space. The input space is designed from knowledge of those variables that affect the behaviour of the output parameter. For ionospheric parameters this input space would always include a solar variable due to the strong influence that the sun has on ionospheric behaviour.     

Comparison of model and experimental ionospheric parameters at high latitudes

Modern use and study of the auroral region needs to attract a wider class of models for describing conditions of radio wave propagation in the ionosphere. In this paper the possibilities of the International Reference Ionosphere model, well-proven and widespread in the mid-latitudes, are investigated in the high latitude zone. Model and measured values of the critical frequency foF2 for two mid-latitude stations (Juliusruh and Goosebay) and four high-latitude ones (Loparskaya, Sodankyla, Sondrestrom, Thule) are compared. Deviations of medians, variations from day to day and solar activity trends seemed to be similar for both areas. This similarity is irrespective of the RZ12 index. Special attention is paid to the TEC parameter and its determination using 6 versions of models, a new version of the model IRI2010 (IRI-Plas) among them. It is shown that the IRI-Plas model significantly improves the definition of TEC in contrast to the versions of IRI2007 and the new model NeQuick. The use of the median of the experimental equivalent slab thickness, together with the current values of the TEC, increases by a factor of two the agreement between calculated and measured foF2 values as compared with the variations from day to day. This allows foF2 to be defined in near-real time.     

A 12 year comparison of MIDAS and IRI 2007 ionospheric Total Electron Content

Data assimilation in conventional meteorological applications uses measurements in conjunction with a physical model. In the case of the ionised region of the upper atmosphere, the ionosphere, assimilation techniques are much less mature. The empirical model known as the International Reference Ionosphere (IRI) could be used to augment data-sparse regions in an ionospheric now-cast and forecast system. In doing so, it is important that it does not introduce systematic biases to the result. Here, the IRI model is compared to ionospheric observations from the Global Positioning System satellites over Europe and North America. Global Positioning System data are processed into hour-to-hour monthly averages of vertical Total Electron Content using a tomographic technique. A period of twelve years, from January 1998 to December 2009, is analysed in order to capture variations over the whole solar cycle. The study shows that the IRI model underestimates Total Electron Content in the daytime at solar maximum by up to 37% compared to the monthly average of GPS tomographic images, with the greatest differences occurring at the equinox. IRI shows good agreement at other times. Errors in TEC are likely due to peak height and density inaccuracies. IRI is therefore a suitable model for specification of monthly averages of Total Electron Content and can be used to initialise a data assimilation process at times away from solar maximum. It may be necessary to correct for systematic deviations from IRI at solar maximum, and to incorporate error estimation into a data assimilation scheme.     

Prediction of ionospheric total electron content using adaptive neural network with in-situ learning algorithm

The Ionospheric Total Electron Content is responsible for the group delay of the signals from the Navigation satellites. This delay causes ranging error, which in turn degrades the accuracy of position estimated by the receivers. For critical applications, single frequency receivers resort to Satellite Based Augmentation Systems in order to have improved accuracy and integrity. The performance of these systems in terms of accuracy can be improved if predictions of the delays are available simultaneously with real measurements. This paper attempts to predict the Total Electron Content using adaptive recurrent Neural Network at three different locations of India. These locations are selected at the magnetic equator, at the equatorial anomaly crest and outside the anomaly range, respectively. In-situ Learning Algorithm has been used for tracking the non-stationary nature of the variation. Prediction is done for different prediction intervals. It is observed that, for each case, the mean and root mean square values of prediction errors remain small enough for all practical applications. Analysis of Variance is also done on the results.     

Statistical ionospheric E layer properties measured with the Cyprus Digisonde and comparisons with IRI predictions

This paper reports the diurnal, seasonal, and long term variability of the E layer critical frequency (foE) and peak height (hmE) derived from Digisonde measurements from 2009 to 2016 at the low-middle latitude European station of Nicosia, Cyprus (geographical coordinates: 35°N, 33°E, geomagnetic lat. 29.38°N, I = 51.7°). Manually scaled monthly median values of foE and hmE are compared with IRI-2012 predictions with a view to assess the predictability of IRI. Results show that in general, IRI slightly overestimates foE values both at low and high solar activity. At low solar activity, overestimations are mostly limited to 0.25?MHz (equivalent electron density, 0.775?×?10³?el/m^?3) but can go as high as 0.5?MHz (equivalent electron density, 3.1?×?10³?el/m^?3, during noon) around equinox. In some months, underestimations, though sporadic in nature, up to 0.25?MHz are noted (mostly during sunrise and sunset). At high solar activity, a similar pattern of over-/underestimation is evident. During the entire period of study, over-/under estimations are mostly limited to 0.25?MHz. In very few cases, these exceed 0.25?MHz but are limited to 0.5?MHz. Analysis of hmE reveals that: (1) hmE remains almost constant during ±2 to ±4?h around local noon, (2) hmE values are higher in winter than in spring, summer and autumn, (3) there are two maxima near sunrise and sunset with a noontime minimum in between. During the entire period of study, significant differences between observed hmE and the IRI predictions have been noted. IRI fails to predict hmE and outputs a constant value of 110?km, which is higher than most of the observed values. Over- and under estimations range from 3 to 13?km and from 0 to 3?km respectively.     

Evaluation of the STORM model storm-time corrections for middle latitude

This paper presents results from the Storm-Time Ionospheric Correction Model (STORM) validation for selected Northern and Southern Hemisphere middle latitude locations. The created database incorporated 65 strong-to-severe geomagnetic storms, which occurred within the period 1995–2007. This validation included data from some ionospheric stations (e.g., Pruhonice, El Arenosillo) that were not considered in the development or previous validations of the model. Hourly values of the F2 layer critical frequency, foF2, measured for 5–7 days during the main and recovery phases of each selected storm were compared with the predicted IRI 2007 foF2 with the STORM model option activated. To perform a detailed comparison between observed values, medians and predicted foF2 values the correlation coefficient, the root-mean-square error (RMSE), and the percentage improvement were calculated. Results of the comparative analysis show that the STORM model captures more effectively the negative phases of the summer ionospheric storms, while electron density enhancement during winter storms and the changeover of the different storm phases is reproduced with less accuracy. The STORM model corrections are less efficient for lower-middle latitudes and severe geomagnetic storms.     

A new global version of M(3000)F2 prediction model based on artificial neural networks

A new version of global empirical model for the ionospheric propagation factor, M(3000)F2 prediction is presented. Artificial neural network (ANN) technique was employed by considering the relevant geophysical input parameters which are known to influence the M(3000)F2 parameter. This new version is an update to the previous neural network based M(3000)F2 global model developed by Oyeyemi et al. (2007), and aims to address the inadequacy of the International Reference Ionosphere (IRI) M(3000)F2 model (the International Radio Consultative Committee (CCIR) M(3000)F2 model). The M(3000)F2 has been found to be relatively inaccurate in representing the diurnal structure of the low latitude region and the equatorial ionosphere. In particular, the existing hmF2 IRI model is unable to reproduce the sharp post-sunset drop in M(3000)F2 values, which correspond to a sharp post-sunset peak in the peak height of the F2 layer, hmF2. Data from 80 ionospheric stations globally, including a good number of stations in the low latitude region were considered for this work. M(3000)F2 hourly values from 1987 to 2008, spanning all periods of low and high solar activity were used for model development and verification process. The ability of the new model to predict the M(3000)F2 parameter especially in the low latitude and equatorial regions, which is known to be problematic for the existing IRI model is demonstrated.     

Linkage of the ionospheric peak electron density and height deduced from the topside sounding data

Topside sounding electron density profiles are analyzed to explore interrelations of the F2 layer critical frequency and the peak height for a representative set of conditions provided by ISIS1, ISIS2, IK19 and Cosmos-1809 satellites for the period of 1969–1987. The foF2 and hmF2 are delivered with exponential extrapolation of electron density profile to zero of its 1st derivative. It is shown that the linear regression exists between foF2 and hmF2 under different conditions. The linkage between the two parameters amended to the empirical model of the peak height [Gulyaeva, T.L., Bradley, P.A., Stanislawska, I., Juchnikowski, G. Towards a new reference model of hmF2 for IRI. Adv. Space Res. 42, 666–672, doi:10.1016/j.asr.2008.02.021, 2008] results in an empirical model of the both foF2 and hmF2 expressed by superposition of functions in terms of local-time, season, geodetic longitude, modified dip latitude and solar activity. For the solar activity we use a proxy Fsp index averaged from the mean solar radio flux F10.7s for the past 81 days (3 solar rotations) and F10.7 value for 1 day prior the day of observation. Impact of geomagnetic activity is not discernible with the topside sounding data due to mixed positive and negative storm-time effects. Appreciable differences have been revealed between IRI-CCIR predictions and outcome of the new model which might be attributed to the different techniques of the peak electron density and height derivation, different epochs and different global distribution of the source data as well as the different mathematical functions involved in the maps and the model presentation.     

Towards a GPS-based TEC prediction model for Southern Africa with feed forward networks

In this paper, first results from a national Global Positioning System (GPS) based total electron content (TEC) prediction model over South Africa are presented. Data for 10 GPS receiver stations distributed through out the country were used to train a feed forward neural network (NN) over an interval of at most five years. In the NN training, validating and testing processes, five factors which are well known to influence TEC variability namely diurnal variation, seasonal variation, magnetic activity, solar activity and the geographic position of the GPS receivers were included in the NN model. The database consisted of 1-min data and therefore the NN model developed can be used to forecast TEC values 1 min in advance. Results from the NN national model (NM) were compared with hourly TEC values generated by the earlier developed NN single station models (SSMs) at Sutherland (32.38°S, 20.81°E) and Springbok (29.67°S, 17.88°E), to predict TEC variations over the Cape Town (33.95°S, 18.47°E) and Upington (28.41°S, 21.26°E) stations, respectively, during equinoxes and solstices. This revealed that, on average, the NM led to an improvement in TEC prediction accuracy compared to the SSMs for the considered testing periods.     

Equatorial predictions from a new neural network based global foF2 model

A new neural network (NN) based global empirical model for the foF2 parameter, which represents the peak ionospheric electron density, has been developed using extended temporal and spatial geophysical relevant inputs. It has been proposed that this new model be considered as a suitable replacement for the International Union of Radio Science (URSI) and International Radio Consultative Committee (CCIR) model options currently used within the International Reference Ionosphere (IRI) model for the purpose of F2 peak electron density predictions. The most recent version of the model has incorporated data from 135 global ionospheric stations including a number of equatorial stations.     

A prediction model of short-term ionospheric foF2 based on AdaBoost

In this paper, the AdaBoost-BP algorithm is used to construct a new model to predict the critical frequency of the ionospheric F2-layer (foF2) one hour ahead. Different indices were used to characterize ionospheric diurnal and seasonal variations and their dependence on solar and geomagnetic activity. These indices, together with the current observed foF2 value, were input into the prediction model and the foF2 value at one hour ahead was output. We analyzed twenty-two years’ foF2 data from nine ionosonde stations in the East-Asian sector in this work. The first eleven years’ data were used as a training dataset and the second eleven years’ data were used as a testing dataset. The results show that the performance of AdaBoost-BP is better than those of BP Neural Network (BPNN), Support Vector Regression (SVR) and the IRI model. For example, the AdaBoost-BP prediction absolute error of foF2 at Irkutsk station (a middle latitude station) is 0.32 MHz, which is better than 0.34 MHz from BPNN, 0.35 MHz from SVR and also significantly outperforms the IRI model whose absolute error is 0.64 MHz. Meanwhile, AdaBoost-BP prediction absolute error at Taipei station from the low latitude is 0.78 MHz, which is better than 0.81 MHz from BPNN, 0.81 MHz from SVR and 1.37 MHz from the IRI model. Finally, the variety characteristics of the AdaBoost-BP prediction error along with seasonal variation, solar activity and latitude variation were also discussed in the paper.     

A new global F2 peak electron density model for the International Reference Ionosphere (IRI)

A new neural network (NN) based global empirical model for the F2 peak electron density (NmF2) has been developed using extended temporal and spatial geophysical relevant inputs. Measured ground based ionosonde data, from 84 global stations, spanning the period 1995 to 2005 and, for a few stations from 1976 to 1986, obtained from various resources of the World Data Centre (WDC) archives (Space Physics Interactive Data Resource SPIDR, the Digital Ionogram Database, DIDBase, and IPS Radio and Space Services) have been used for training a NN. The training data set includes all periods of quiet and disturbed magnetic activity. A comprehensive comparison for all conditions (e.g., magnetic storms, levels of solar activity, season, different regions of latitudes, etc.) between foF2 value predictions using the NN based model and International Reference Ionosphere (IRI) model (including both the International Union of Radio Science (URSI) and International Radio Consultative Committee (CCIR) coefficients) with observed values was investigated. The root-mean-square (RMS) error differences for a few selected stations are presented in this paper. The results of the foF2 NN model presented in this work successfully demonstrate that this new model can be used as a replacement option for the URSI and CCIR maps within the IRI model for the purpose of F2 peak electron density predictions.     

Diurnal and seasonal variation of F2-layer ionospheric parameters at equatorial ionization anomaly crest region and their comparison with IRI-2001

Diurnal and seasonal variations of critical frequency of ionospheric F2-region ‘foF2’ and the height of peak density ‘hmF2’ are studied using modern digital ionosonde observations of equatorial ionization anomaly (EIA) crest region, Bhopal (23.2°N, 77.6°E, dip 18.5°N), during solar minimum period 2007. Median values of these parameters are obtained at each hour using manually scaled data during different seasons and compared with the International Reference Ionosphere-2001 model predictions. The observations suggest that on seasonal basis, the highest values of foF2 are observed during equinox months, whereas highest values of hmF2 are obtained in summer and lowest values of both foF2 and hmF2 are observed during winter. The observed median and IRI predicted values of foF2 and hmF2 are analyzed with upper and lower bound of inter-quartile range (IQR) and it is find out that the observed median values are well inside the inter-quartile range during the period of 2007. Comparison of the recorded foF2 and hmF2 values with the IRI-2001 output reveals that IRI predicted values exhibit better agreement with hmF2 as compared to foF2. In general, the IRI model predictions show some agreement with the observations during the year 2007. Therefore it is still necessary to implement improvements in order to obtain better predictions for EIA regions.     

A steady-state model for the D- to F-region of the polar cap

For obvious reasons the ionosphere of the polar cap, surrounded by the auroral zone, is only poorly investigated. Even ionosonde data are very scant from geomagnetic latitudes beyond 70°. Since 1997 the European incoherent scatter radar facility EISCAT has an additional installation on Svalbard and has been providing electron density data nearly continuously ever since. These measurements which mainly cover the E- and F-regions are supplemented by rocket data from Heiss Island at a comparable magnetic latitude; these data are more sporadic, but cover lower altitudes and densities. A provisional, steady-state, neural network-based model is presented which uses the data of both sites.     

An empirical model of electron density in low latitude at 600 km obtained by Hinotori satellite

An empirical model of electron density (Ne) was constructed by using the data obtained with an impedance probe on board Japanese Hinotori satellite. The satellite was in circular orbit of the height of 600 km with the inclination of 31 degrees from February 1981 to June 1982. The constructed model gives Ne at any local time with the time resolution of 90 min and between −25 and 25 degrees in magnetic latitude with its resolution of 5 degrees in the range of F_10.7 from 150 to 250 under the condition of K_p < 4. Spline interpolations are applied to the functions of day of year, geomagnetic latitude and solar local time, and linear interpolation is applied to the function of F_10.7. Longitude dependence of Ne is not taken into account. Our density model can reproduce solar local time variation of electron density at 600 km altitude better than current International Reference Ionosphere (IRI2001) model which overestimates Ne in night time and underestimates Ne in day time. Our density model together with electron temperature model which has been constructed before will enable more understanding of upper ionospheric phenomenon in the equatorial region.     

Accuracy of IRI profiles of ionospheric density and temperatures derived from comparisons to Kharkov incoherent scatter radar measurements

The incoherent scatter radar (ISR) facility in Kharkov, Ukraine (49.6°N, 36.3°E) measures vertical profiles of electron density, electron and ion temperature, and ion composition of the ionospheric plasma up to 1100 km altitude. Acquired measurements constitute an accurate ionospheric reference dataset for validation of the variety of models and alternative measurement techniques. We describe preliminary results of comparing the Kharkov ISR profiles to the international reference ionosphere (IRI), an empirical model recognized for its reliable representation of the monthly-median climatology of the density and temperature profiles during quiet-time conditions, with certain extensions to the storm times. We limited our comparison to only quiet geomagnetic conditions during the autumnal equinoxes of 2007 and 2008. Overall, we observe good qualitative agreement between model and data both in time and with altitude. Magnitude-wise, the measured and modeled electron density and plasma temperatures profiles appear different. We discovered that representation accuracy improves significantly when IRI is driven by observed-averaged values of the solar activity index rather than their predictions. This result motivated us to study IRI performance throughout protracted solar minimum of the 24th cycle. The paper summarizes our observations and recommendations for optimal use of the IRI.     

Using the radial basis function neural network to predict ionospheric critical frequency of F2 layer over Wuhan

Neural networks (NNs) have been applied to ionospheric predictions recently. This paper uses radial basis function neural network (RBF-NN) to forecast hourly values of the ionospheric F₂ layer critical frequency(f_oF₂), over Wuhan (30.5N, 114.3E), China. The false nearest neighbor method is used to determine the embedding dimension, and the principal component analysis (PCA) is used to reduce noise and dimension. The whole study is based on a sample of about 26,000 observations of f_oF₂ with 1-h time resolution, derived during the period from January 1981 to December 1983. The performance of RBF-NN is estimated by calculating the normalized root-mean-squared (NRMSE) error, and its results show that short-term predictions of f_oF₂ are improved.     

Correlation of IRTAM and FPMU data confirming the application of IRTAM to support ISS Program safety

A “Real-Time” plasma hazard assessment process was developed to support International Space Station (ISS) Program real-time decision-making providing solar array constraint relief information for Extravehicular Activities (EVAs) planning and operations. This process incorporates real-time ionospheric conditions, ISS solar arrays’ orientation, ISS flight attitude, and where the EVA will be performed on the ISS. This assessment requires real-time data that is presently provided by the Floating Potential Measurement Unit (FPMU) which measures the ISS floating potential (FP), along with ionospheric electron number density (Ne) and electron temperature (Te), in order to determine the present ISS environment. Once the present environment conditions are correlated with International Reference Ionosphere (IRI) values, IRI is used to forecast what the environment could become in the event of a severe geomagnetic storm. If the FPMU should fail, the Space Environments team needs another source of data which is utilized to support a short-term forecast for EVAs. The IRI Real-Time Assimilative Mapping (IRTAM) model is an ionospheric model that uses real-time measurements from a large network of digisondes to produce foF2 and hmF2 global maps in 15?min cadence. The Boeing Space Environments team has used the IRI coefficients produced in IRTAM to calculate the Ne along the ISS orbital track. The results of the IRTAM model have been compared to FPMU measurements and show excellent agreement. IRTAM has been identified as the FPMU back-up system that will be used to support the ISS Program if the FPMU should fail.