Empirical Orthogonal Function Model Research Articles

Modeling TEC Irregularities in the Arctic Ionosphere Using Empirical Orthogonal Function Method

AbstractWe develop a climatological model for the Arctic ionosphere based on more than one solar cycle of data (2010–2021) of the rate of change of the total electron content index (ROTI) maps from the International GNSS Service (IGS). The IGS ROTI maps are daily averaged in magnetic latitude and local time coordinates. To develop a climatological model, the ROTI maps are decomposed into base functions and coefficients using the empirical orthogonal function (EOF) method. The EOF method converges very quickly, and the first four EOFs reflect the majority (96%) of the total data variability. Furthermore, different EOF components can reflect different drivers of ionospheric irregularities. The first EOF reflects the averaged ROTI activity and the impact of the solar radiation and geomagnetic activity; the second EOF reflects the impact of the interplanetary magnetic field (IMF) Bz and electric field; the third and fourth EOFs reflect the dawn‐dusk asymmetry around the auroral oval and polar cap, and they can be related to the IMF By. To build an empirical model, we fit the EOF coefficients using helio‐geophysical indices from four different categories (solar activity; geomagnetic indices; IMF; the solar wind coupling function). The final EOF model is dependent on seven selected indices (F10.7P, Kp, Dst, Bt, By, Bz, and EKL). The statistical data‐model comparisons show satisfactory results with a good correlation coefficient. However, the model cannot capture the significant expansion of the dayside ROTI activity during strong geomagnetic storms. Future effort is needed to provide corrections to the model during severe storms.

A Model of High Latitude Ionospheric Convection Derived From SuperDARN EOF Model Data

AbstractForecasting of the effects of thermospheric drag on satellites will be improved significantly with better modeling of space weather effects on the high‐latitude ionosphere, in particular the Joule heating arising from electric field variability. We use a regression analysis to build a model of the ionospheric convection drift velocity which is driven by relatively few solar and solar wind variables. The model is developed using a solar cycle's worth (1997–2008 inclusive) of 5‐min resolution Empirical Orthogonal Function (EOF) patterns derived from Super Dual Auroral Radar Network (SuperDARN) line‐of‐sight observations of the convection velocity across the high‐latitude northern hemisphere ionosphere. At key stages of development of the model, we use the percentage of explained variance P to see how well the model reproduces the EOF data. The final model is driven by four variables: (a) the interplanetary magnetic field component By, (b) the solar wind coupling parameter epsilon ε, (c) a trigonometric function of day‐of‐year, and (d) the monthly F10.7 index. The model can reproduce the EOF velocities with a characteristic P = 0.7. The model and EOF data compare best around the solar maximum of 2001. is lower around solar minimum, due to occasional limitations in the geographical and temporal coverage of the SuperDARN measurements. This may indicate the need to modify our model around the minimum of the solar cycle. Our model has the potential to be used to forecast the ionospheric electric field using the real‐time solar wind data available from spacecraft located upstream of the Earth.

Ionospheric Current Variations by Empirical Orthogonal Function Analysis: Solar Activity Dependence and Longitudinal Differences

AbstractThe solar quiet (Sq) ionospheric current variations exhibit spatial and temporal patterns that can be identified by the prevailing eigenmodes based on the empirical orthogonal function (EOF) analysis. In this study, the Sq current function over the American and European/African sectors are derived using ground magnetometer data from 2006 to 2019 based on the spherical harmonic analysis technique. Subsequently, we decomposed the Sq current function into eigenmodes by applying the EOF analysis, where the first three eigenmodes capture 96% of the overall Sq current variance. Additionally, these eigenmodes are utilized to model the Sq current function and compare its properties between the two longitudinal sectors. We observed that the EOF model could reconstruct the observed Sq current function with the first three eigenmodes in both longitudinal sectors. Moreover, the EOF model unveils a clear association of the Sq current function with several driven features, such as magnetic latitude, local time, season, and solar activity. Both longitudinal sectors had comparable Sq current patterns under varying solar activity, while their amplitudes varied. Besides, the newly developed model could reproduce a refined Sq current variability over the two longitudinal sectors as long as the observed Sq variations have sufficient duration. Our EOF model shows that the variations of the Sq current function with solar activity can be explained by the first three eigenmodes, which could be used as a basis for further numerical modeling of the Sq current variations.

Empirical Modeling of Ionospheric Current Using Empirical Orthogonal Function Analysis and Artificial Neural Network

AbstractGiven the potential importance of solar quiet (Sq) ionospheric current in geomagnetic field modeling, it is vital to obtain accurate parameters characterizing its variations, particularly the spatial and temporal variations. In this paper, we derived the Sq current function based on the spherical harmonic analysis (SHA) technique using a 14‐year (2006–2019) quiet geomagnetic field record over the American sector. The empirical orthogonal function (EOF) analysis was then applied to deduce temporal and spatial variations of the Sq current. It is observed that the first EOF mode of the Sq current function is dominated by solar activity, while the second and third EOF modes exhibit annual and semiannual variations, respectively. Also, the artificial neural network (ANN) model of Sq current function was constructed to validate the EOF model predictions. While the Sq current intensity predicted by the ANN model is underestimated by 2.83%, the EOF model underpredicted the Sq current intensity by 1.92% relative to the observation. The root mean square error (RMSE) of the EOF model is 0.64 kA. This RMSE is about 79% smaller than that of the ANN model. In addition, both the EOF and ANN models capture the variation of the total Sq current (Jtotal) intensity with respect to solar activity. In principle, the EOF model had an optimal performance at nearly 98% accuracy, with the ANN model exhibiting almost the same degree of accuracy, which appears to be a reference point for ionospheric conditions when looking for space weather applications.

Advanced Machine Learning Techniques for Predicting Nha Trang Shorelines

Nha Trang Coast is located in the South Central Vietnam and the coastal erosion has occurred rapidly in recent years. Hence it is crucial to accurately monitor the shoreline changes for better coastal management and reduction of risks for communities. In this paper, we explored a statistical forecasting model, Seasonal Auto-regressive Integrated Moving Average (SARIMA), and two Machine Learning (ML) models, Neural Network Auto-Regression (NNAR) and Long Short-Term Memory (LSTM), to predict the shoreline variations from surveillance camera images. Compared to the Empirical Orthogonal Function (EOF), the most common method used for predicting shoreline changes from cameras, we demonstrate that the SARIMA, NNAR and LSTM models outperform the EOF model significantly in terms of prediction accuracy. The forecasting performance of the SARIMA model, NNAR model and LSTM model is comparable in both long and short-term predictions. The results suggest that these models are highly effective in detecting shoreline changes from video cameras under extreme weather conditions.

The variation of ionosonde-derived hmF2 and its comparisons with International Reference Ionosphere (IRI) and Empirical Orthogonal Function (EOF) over Pakistan longitude sector during solar cycle 22

Variations of maximum height of F2 ionospheric layer are analysed over ionospheric stations of Pakistan located at Islamabad (geog. coord. 33.75°N, 72.87°E), Multan (30.18°N, 71.48°E) and Karachi (24.95°N, 67.14°E) during the years, 1987 (LSA), 1990 (HSA) and 1993 (MSA) representing low, high and moderate solar activity years, respectively. Results showed that hmF2 in summer is higher than in winter during LSA and MSA at all stations. However, diurnal pattern is not consistently followed during winters of LSA and MSA. The lowest hmF2 values are observed around sunrise and sunset; whereas, higher values are observed around noon and midnight which may be due to upward and downward plasma drift velocity as diurnal behaviour of hmF2 is similar to diurnal behaviour of E×B drift. No specific latitudinal trend is observed in hmF2 during the period of this study over Pakistan which may be due to the combined effect of E×B drift and energy transferred to ionosphere by atmospheric planetary waves. Solar quiet current seems responsible for the variation of hmF2 over Multan and Islamabad. For Karachi equatorial electrojet seems controlling the daytime hmF2 during LSA. The hmF2 is found to have linear correlation with solar activity and this correlation is stronger with solar index F10.7 as compared to the sunspot numbers. The correlation coefficients for both solar indices are above 80%; whereas, geomagnetic indices Ap and Kp are weakly correlated having correlation coefficients less than 30%. Ionosonde-derived hmF2 are compared with regional model based on expansion of Empirical Orthogonal Function (EOF) with linear and spline interpolation of coefficients of time, seasons, magnetic dip & sunspot numbers and, global model, International Reference Ionosphere (IRI), with International Union of Radio Science (URSI) and Consultative Committee for International Radio (CCIR) options of IRI-2012 and AMTB-2013, SHU-2015 and BSE-1979 sub-models in combination with URSI and CCIR of IRI-2016 versions. The daytime hmF2 values over Pakistan modelled by AMTB of IRI-2016 (with URSI and CCIR) are found to be the most converging of all IRI options during all solar periods. AMTB-2013 also predicted nighttime values with least errors in most cases except during LSA. In addition, IRI showed better equinoctial and annual correlations with ionosonde-derived hmF2 as compared to EOF model. EOF based model showed higher nighttime Mean Absolute Errors (MAE) as compared to IRI. The lowest daytime and nighttime errors in hmF2 are observed over Multan during LSA shown by IRI-2016-AMTB-2013 (using URSI and CCIR) with MAE being 7.8 km and IRI-2016-SHU-2015 (using URSI and CCIR) with MAE being 4.7 km.

Empirical orthogonal function modelling of total electron content over Nepal and comparison with global ionospheric models

This analysis uses 3 years hourly observations of total electron content (TEC) from 5 global positioning system (GPS) station across Nepal to analyze the spatial trend. For this purpose, empirical orthogonal function modeling is used to investigate the annual and monthly variation inside the country. Empirical orthogonal function base functions and associated coefficients of TEC variability over Nepal have been studied to establish the relationship between observed and modeled TEC values. Both the observed GPS TEC values and the empirical orthogonal function modeled TEC values are compared with the global ionospheric models (global ionospheric map and international reference ionosphere) TEC values. The study shows an hourly pattern of TEC variation in which the TEC rises from dawn, reaches the highest TEC values about 40 TEC units during the peak hours of the day, then decreases at evening at the lowest diurnal values about 5 TEC units. Monthly TEC values over all sites are higher during the march and April (about 38 TEC unit), while they are lower values during December and January (about 10 TEC unit). Although the correlation coefficients between the GPS TEC values and the global modeled TEC values are higher, while it becomes highest with empirical orthogonal function modeled TEC values for both cases of hourly and monthly variations. We examined the root mean square errors between observed and modeled TEC values at each site by using tailor correlation plots and found that they are lower in case of empirical orthogonal function model. Monthly residuals between observed and empirical orthogonal function modeled TEC values are always lower as compared to other global modeled TEC values. These kinds of comparative analysis in the present work indicate that empirical orthogonal function model by using global geomagnetic activity works very well and is capable of depicting TEC variations accurately.

Empirical orthogonal function analysis and modeling of global ionospheric spherical harmonic coefficients

We developed a global empirical model for computing spherical harmonic (SH) coefficients based on the empirical orthogonal function (EOF) method and periodic functions by utilizing global ionospheric SH coefficients data provided by Center for Orbit Determination in Europe (CODE) during the years 2005–2016. Results show that the first four-order base functions and corresponding associated coefficients can represent 97.15% of the basic characteristics of the original data. The first four-order associated coefficients have noticeable periodic variations, and the correlation between these coefficients and the solar activity intensity is high. By fitting the associated coefficients with the periodic function that takes into account the influence of solar activity, it is possible to establish an EOF model to characterize the variations of the ionospheric SH coefficients with few model parameters and further calculate the global vertical total electron content (VTEC). Relative to the existing global VTEC EOF models, this EOF method can achieve high-accuracy modeling of global VTEC with a smaller number of model coefficients. By comparing the SH coefficients and the global VTEC between the EOF model and CODE, results demonstrate that the EOF model can achieve high accuracy and reliability under different solar activities. The difference between the EOF model and CODE is basically at the same level as that between the individual ionospheric analysis centers and CODE. In the extreme event of magnetic storms, the EOF model can also present higher accuracy than the international reference ionosphere (IRI) model.

Research on Short-term Ionospheric Prediction Combining with EOF and ARIMA Model Over Guangxi Area

Abstract. According to the empirical orthogonal function (EOF), the non-stationary time series data are decomposed into time function and space function, so this mathematical method can simplify the non-stationary time series and eliminate redundant information, thus it performs well in non-stationary time series analysis. The ionospheric Vertical Total Electron Content (VTEC) is a non-stationary time series, which has non-stationary and seasonal variation and the activity of VTEC is more active in low latitudes. Guangxi is located in the middle and low latitudes of the Northern Hemisphere with abundant sunshine in summer and autumn. The energy released by solar radiation makes the ionospheric activity in this region more complex than that in the high latitudes. However, no expert or scholar has used EOF analysis method to conduct a comprehensive study of the low latitudes. The International GNSS Service (IGS) provided by high precision Global Ionospheric Maps (GIM) center in Guangxi are used in the modeling data, the GIM data of the first 10 days of different seasons are decomposed by EOF, and then the time function is predicted by ARIMA model. VTEC values for the next five days are obtained through reconstruction, and relative accuracy and standard deviation are used as accuracy evaluation criteria. The results of EOF-ARIMA model are compared with those of ARIMA model, and the prediction accuracy of EOF-ARIMA model at the equatorial anomaly is analyzed in order to explore the reliability of the model in the more complex region of ionospheric activity. The results show that the average relative precision of EOF-ARIMA model is 84.0, the average standard deviation is 7.45TECu, the average relative precision of ARIMA model is 81.5, the average standard deviation is 8.29TECu, and the precision of EOF-ARIMA model is higher than that of ARIMA model.; There is no significant seasonal difference in the prediction accuracy of EOF-ARIMA model, and the prediction accuracy of ARIMA model in autumn is lower than that of other seasons, which indicates that the prediction results of EOF-ARIMA model are more reliable; The prediction accuracy of the EOF-ARIMA model at the equatorial anomaly is not affected, and it is consistent with the accuracy of the high latitude area in Guangxi. It is shown that the EOF-ARIMA model has high accuracy and stability in the short-term ionospheric prediction in Guangxi at low latitudes of China, and provides a new and reliable method for ionospheric prediction at low latitudes.

Cokriging based statistical approximation model for forecasting ionospheric VTEC during high solar activity and storm days

The ionospheric storm is a space climate based event that takes place as a function of time, season and location. In spite of that, it is not yet possible to state how the ionosphere will react to a given space climate event since the measurements of the location, time of observation, amount of disturbances, and type of storm vary from event to event. Nevertheless, statistical analysis of observations in terms of Total Electron Content (TEC) enables one to calculate and forecast a most likely upcoming disturbed TEC, based on predictions of geomagnetic activity. The forecast of disturbed TEC is important and it helps users to know how much it affects the satellite communication systems. In this paper, GPS Vertical TEC (VTEC) data during ionospheric storm has been analyzed and storm-influenced features in the VTEC have been studied. Input parameters such as, location (Latitude & Longitude), Time, F10.7, Ap and Dst indices are collected from NASA website and its corresponding TEC values are used for construction of Cokriging (COK) based statistical approximation model. Prediction of VTEC is performed during storm and high solar activity days and for this purpose previous one-week data of different regions are used. The VTEC prediction is performed using COK model during high solar activity (2015) for IISC station. From the prediction, it is found that, our proposed COK model gives good prediction with RMSE of 6.5325 TECU, Correlation Coefficient as 0.9643 and Mean accuracy of 5.1752 TECU. Also VTEC prediction is performed over three different latitude regions during storm days (2003) and from the predicted results it is noted that, in high latitude region RMSE is 6.1848 TECU, correlation coefficient is 0.3958 and mean accuracy is 4.8105 TECU, in mid latitude RMSE is 12.7957 TECU, correlation coefficient is 0.9249 and mean accuracy is 9.2674 TECU and in low latitude RMSE is 11.5348 TECU, correlation coefficient is 0.9299 and mean accuracy is 9.2116 TECU. The results show that COK model provides good forecasting at low and mid latitude regions. Finally, prediction results of COK model is compared with the Empirical Orthogonal Function (EOF) and IRI-Plas-2017 models over Sutherland (−32.21°N, 20.81°E) station in South Africa during storm conditions. It is found that the average RMSE of EOF model is 5.91 TECU, average RMSE of the IRI-Plas-2017 model is 8.2079 TECU and average RMSE of COK model is 5.5971 TECU. Hence the prediction results show that COK model performs 5.6% better than the EOF model and 46.64% better than the IRI-Plas-2017 model. These results of the proposed COK model is encouraging and useful for indicating storm and high solar activity.

Empirical Orthogonal Function analysis and modeling of ionospheric TEC over South Korean region

This paper presents the ionospheric Total Electron Content (TEC) variations over the low-middle latitude South Korean region using dual frequency Global Navigation Satellite System (GNSS) observations from 14 permanent stations with the data spanning approximately eight years (January 2010 to December 2017). Although, significant work has been conducted in the Korean territory on high-precision positioning, surveying, natural disaster mitigation, and reference frame and datum definition; however, there is substantial scope for modeling of the low-middle latitude ionosphere over the region, which would provide further navigational and communicational benefits. Therefore, in this study, we investigated spatial and temporal TEC variations in GNSS observables through Empirical Orthogonal Function (EOF) modeling and substantiate our findings against existing empirical International Reference Ionosphere (IRI-2016) and NeQuick-2 models. In addition, observation and modeling studies conducted during a geomagnetic storm period (3–9 September, 2017), when the vertical TEC (VTEC) value was almost double that of its regular level, confirm the superior performance of the EOF model in the percentage deviation and correlation plots. To ascertain the performance of the EOF model, the geomagnetic coordinates and PCN index were considered in this study along with other solar and geomagnetic indices (F10.7, Ap and Dst). Analysis of results emphasizes the superior performance of the EOF model compared to other regional and global models with respect to its accuracy and quality relating to quick convergence of decomposition modes and discrimination of temporal as well as spatial components.

A study of the ionospheric disturbances associated with strong earthquakes using the empirical orthogonal function analysis

In this study, an ionospheric logTEC model has been constructed using an empirical orthogonal function (EOF) decomposition method. The main orders (1–9 orders) of this EOF model represent the ionospheric background, while the rest high orders represent ionospheric TEC perturbations. Based on this model, logTEC data during 16 Ms ≥ 8.0 earthquakes from 2000 to 2012 have been analyzed. We found that ionospheric disturbances occurred in 10 earthquakes. Ionospheric abnormities were clearly observed 5 days before the earthquakes, but ionospheric disturbances can also be seen 1 day before, and 1 day and 2 days after the earthquakes. For the TEC data, the possibility of positive (enhanced TEC) and negative (decreased TEC) abnormities is almost the same. Furthermore, by using the simulation results of ionospheric electric field and SAMI2 model, we show that an abnormal westward electric field can lead to electron density enhancements equatorward and decrease polarward of the epicenters, and vice versa for an eastward abnormal electric field.

Shoreline and Beach Cusps Dynamics at the Low Tide Terraced Grand Popo Beach, Bénin (West Africa): A Statistical Approach

Bonou, F.; Angnuureng, D.B.; Sohou, Z.; Almar, R.; Alory, G., and du Penhoat, Y., 2018. Shoreline and beach cuspsdynamics at the low tide terraced Grand Popo beach, Benin (West Africa): A statistical approach. In: Almar, R.; Almeida, L.P.; Trung Viet, N., and Sall, M. (eds.), Tropical Coastal and Estuarine Dynamics. Journal of Coastal Research, Special Issue No. 81, pp. 138–144. Coconut Creek (Florida), ISSN 0749-0208.This paper presents the description of a 2-dimensional shoreline and 3-dimensional shoreline behaviour around a ‘storm free’ microtidal beach from a 3-year video observation using empirical orthogonal function (EOF) analysis. The EOF method is applied successfully to delineate 2D and 3D developments that show the beach evolution influenced by the action of waves and tides. The EOF model results are in agreement with measurements that reflect the morphological concepts for the 2D and 3D cases: the first temporal EOF mode which accounts for an overwhelming 80% of shoreline variation reflects the alongshore-averaged cross-shore migration (2D) largely influenced by waves while the higher eigenfunctions with 20% shoreline variation reflect beach deformation/irregularities (3D). Shoreline location is correlated to cross-shore energy flow from waves, while 3D is associated to the longshore energy flow. The influence of wave height increases cross-shore uniform migration and beach seasonality. The results show that with EOF method, beach cusps are clearly identified for 3D developments to be evaluated. Beach cusps are well observed at low tides on video images. Tide and cusps increase the importance of short term events and deformation; at the lowest high tide mark, beach cusps were observed on higher spatial functions of EOF. This indicates that a study of these morphological features as a coupled system, promotes their contribution in predicting 2D and 3D shoreline changes.

Modeling and analysis of GPS-TEC low latitude climatology during the 24th solar cycle using empirical orthogonal functions

The Total Electron Content (TEC) is an essential component describing the temporal and spatial characteristics of the ionosphere. In this paper, an empirical orthogonal function (EOF) model is constructed by using ground based Global Navigational Satellite System (GNSS) TEC observation data at the Bangalore International GNSS Service (IGS) station (geographic – 13.02° N, 77.57° E; geomagnetic latitude 4.4° N) during an extended period (2009–2016) in the 24th solar cycle. EOF model can be decomposed into base functions and its corresponding coefficients. These decomposed modes well represented the influence of solar and geomagnetic activity towards TEC. The first three EOFs modes constitute about 98% of the total variance of the observed data sets. The Fourier Series Analysis (FSA) is carried out to characterize the solar-cycle, annual and semi-annual dependences by modulating the first three EOF coefficients with solar (F10.7) and geomagnetic (Ap and Dst) indices. The TEC model is validated during daytime and nighttime conditions as well as under different solar activity and geomagnetic conditions. A positive correlation (0.85) of averaged daily GPS-TEC with averaged daily F10.7 strongly supports those time-varying characteristics of the ionosphere features depends on the solar activity. Further, the validity and reliability of EOF model is verified by comparing with the GPS-TEC data, and standard global ionospheric models (International Reference Ionosphere, IRI2016 and Standard Plasmasphere-Ionosphere Model, SPIM). The performances of the standard ionosphericmodelsare marked to be relatively better during High Solar Activity (HSA) periods as compared to the Low Solar Activity (LSA) periods.

Association of Taiwan's October rainfall patterns with large-scale oceanic and atmospheric phenomena

The variability of the amount of October rainfall in Taiwan is the highest among all seasons. The October rainfall in Taiwan is attributable to interactions between the northeasterly monsoon and typhoons and their interaction with Taiwan's Central Mountain Range. This study applied long-term gridded rainfall data for defining the major rainfall pattern for October in Taiwan. The empirical orthogonal function Model 1 (80%) of the October rainfall and El Niño Southern Oscillation (ENSO) index exhibited a significant out-of-phase coherence in a 2–4year period band. This is because an easterly flow on the northern edge of an anomalous low-level cyclonic circulation over the South China Sea during a La Niña developing stage increased the occurrence of an autumn cold front and enhanced the northeasterly monsoon toward northern Taiwan. In addition, a southerly flow on the eastern edge of the anomalous cyclone increased the moisture transport from the tropical Pacific toward Taiwan. The warmer sea surface temperature in the South China Sea, Kuroshio, and the subtropical western Pacific, which may have been induced by an ENSO warm phase peak in the preceding winter, promoted the formation of the anomalous low-level cyclonic circulation.

Characterization of ionospheric variability in TEC using EOF and wavelets over low-latitude GNSS stations

Investigation of ionospheric variability is essential for improving the daily ionospheric modeling and forecasting services of Global Navigation Satellite System (GNSS) applications. As India is a low-latitude region, more care has to be taken here to characterize the ionosphere due to irregularities and Equatorial Ionization Anomaly (EIA) conditions. Therefore, an appropriate method is required to diagnose the ionospheric variations during geomagnetic, solar and other disturbances. In this paper, the temporal ionospheric time delay variations were studied based on the Empirical Orthogonal Function (EOF) analysis and wavelet transforms (WT).These analyses were carried out with Total Electron Content (TEC) datasets obtained from three GNSS stations located in low-latitude regions. EOF analysis was performed on the TEC datasets, which were decomposed into a time series of orthogonal eigen values (or base functions) and associated coefficients. EOF base functions and their associated coefficients signify the hourly time variations and the day of the year variations. The results reveal that the first few EOFs represented the majority of TEC variability pertaining to the physical processes of the ionosphere. The accuracy of the EOF model was validated by the evaluation of observational TEC data with International Reference Ionosphere (IRI) 2012 models. The EOF model coefficients for each GNSS station showed a strong correlation with the IRI models and also described the correlation between the impacts of the level of geomagnetic activity on the ionosphere. The correlation coefficients for the first three EOFs were more than 0.95. The phase relationship of ionospheric TEC anomalies, with respect to the geomagnetic indices (Dst), were analyzed by wavelet transforms.

Modelling total electron content during geomagnetic storm conditions using empirical orthogonal functions and neural networks

AbstractIt has been shown in ionospheric research that modelling total electron content (TEC) during storm conditions is a big challenge. In this study, TEC modelling was performed over Sutherland (32.38°S, 20.81°E, 41.09°S geomagnetic), South Africa, during storm conditions, using a combination of empirical orthogonal function (EOF) and regression analyses techniques. The neural network (NN) technique was also applied to the same TEC data set, and its output was compared with TEC modeled using the EOF model. TEC was derived from GPS observations, and a geomagnetic storm was defined for Dst≤−50 nT. The hour of the day and the day number of the year, F10.7p and A indices, were chosen as inputs for the modeling techniques to take into account diurnal and seasonal variation of TEC, solar, and geomagnetic activities, respectively. Both EOF and NN models were developed using GPS TEC data for storm days counted from 1999 to 2013 and tested on different storms. For interpolation, the EOF and NN models were validated on storms that occurred during high and low solar activity periods (storms of 2000 and 2006), while for extrapolation the validation was done for the storms of 2014 and 2015, identified based on the provisional Dst index data. A comparison of the modeled TEC with the observed TEC showed that both EOF and NN models perform well for storms with nonsignificant ionospheric TEC response and storms that occurred during period of low solar activity. For storms with significant TEC response, TEC magnitude is well captured during the nighttime and early morning, but short‐term features, TEC enhancement, and depression are not sufficiently captured by the models. Statistically, the NN model performs 12.79% better than the EOF model on average, over all storm periods considered. Furthermore, it has been shown that the EOF and NN models developed for a specific station can be used to estimate TEC over other locations within a latitudinal and longitudinal coverage of 8.7° and 10.6°, respectively. This is an important result as it reduces the data dimensionality problem for computational purposes.

Modeling Chinese ionospheric layer parameters based on EOF analysis

Using 24-ionosonde observations in and around China during the 20th solar cycle, an assimilative model is constructed to map the ionospheric layer parameters (foF2, hmF2, M(3000)F2, and foE) over China based on empirical orthogonal function (EOF) analysis. First, we decompose the background maps from the International Reference Ionosphere model 2007 (IRI-07) into different EOF modes. The obtained EOF modes consist of two factors: the EOF patterns and the corresponding EOF amplitudes. These two factors individually reflect the spatial distributions (e.g., the latitudinal dependence such as the equatorial ionization anomaly structure and the longitude structure with east-west difference) and temporal variations on different time scales (e.g., solar cycle, annual, semiannual, and diurnal variations) of the layer parameters. Then, the EOF patterns and long-term observations of ionosondes are assimilated to get the observed EOF amplitudes, which are further used to construct the Chinese Ionospheric Maps (CIMs) of the layer parameters. In contrast with the IRI-07 model, the mapped CIMs successfully capture the inherent temporal and spatial variations of the ionospheric layer parameters. Finally, comparison of the modeled (EOF and IRI-07 model) and observed values reveals that the EOF model reproduces the observation with smaller root-mean-square errors and higher linear correlation coefficients. In addition, IRI discrepancy at the low latitude especially for foF2 is effectively removed by EOF model.

Empirical orthogonal function analysis and modeling of the ionospheric peak height during the years 2002–2011

AbstractThe ionospheric peak electron density height (hm) is one of the most important ionospheric parameters characterizing high‐frequency radio wave propagation conditions. In this paper, a global hm model based on the empirical orthogonal function (EOF) analysis method is constructed by using Global Navigation Satellite Systems ionospheric radio occultation measurements from COSMIC and CHAMP as well as global ionosonde data during the years 2002–2011. The variability of hm can be well represented by the several EOF base functions Ek and the corresponding coefficients Pk. The rapid convergence of EOF decomposition makes it possible to use only the first four EOFs components, which express 99.133% of total variance in this study, to construct the empirical model. The variations of hm with respect to the magnetic latitude, local time, season, and solar cycle have been studied, and the EOF‐based hm model has been validated through comparisons with the International Reference Ionosphere (IRI) model and other observation. The evaluations indicate that the EOF and IRI model give better hmF2 at middle and high latitudes than those at low latitudes. Since the limited data were used in the EOF model during high solar activity years, its accuracy degrades to some extent. During nighttime of spring, summer, and winter in the auroral zone, the hm derived from the EOF model may range from 90 to 150 km because of the reduction of hm, which is due to particle precipitation, whereas the IRI model does not include this reduction. During the periods of low solar activity, the F2 peak heights (hmF2) from the EOF model are in good agreement with the observed data, while the IRI model tends to overestimate the hmF2 in the middle and high latitudes.

Reduced rank models for travel time estimation of low order mode pulses

Mode travel time estimation in the presence of internal waves (IWs) is a challenging problem. IWs perturb the sound speed, which results in travel time wander and mode scattering. A standard approach to travel time estimation is to pulse compress the broadband signal, pick the peak of the compressed time series, and average the peak time over multiple receptions to reduce variance. The peak-picking approach implicitly assumes there is a single strong arrival and does not perform well when there are multiple arrivals due to scattering. This article presents a statistical model for the scattered mode arrivals and uses the model to design improved travel time estimators. The model is based on an Empirical Orthogonal Function (EOF) analysis of the mode time series. Range-dependent simulations and data from the Long-range Ocean Acoustic Propagation Experiment (LOAPEX) indicate that the modes are represented by a small number of EOFs. The reduced-rank EOF model is used to construct a travel time estimator based on the Matched Subspace Detector (MSD). Analysis of simulation and experimental data show that the MSDs are more robust to IW scattering than peak picking. The simulation analysis also highlights how IWs affect the mode excitation by the source.