TEC forecasting based on manifold trajectories

In this paper, we present a method for forecasting the ionospheric Total Electron Content (TEC) distribution from the International GNSS Service’s Global Ionospheric Maps. The forecasting system gives an estimation of the value of the TEC distribution based on linear combination of previous TEC maps (i.e., a set of 2D arrays indexed by time), and the computation of a tangent subspace in a manifold associated to each map. The use of the tangent space to each map is justified because it allows modeling the possible distortions from one observation to the next as a trajectory on the tangent manifold of the map. The coefficients of the linear combination of the last observations along with the tangent space are estimated at each time stamp to minimize the mean square forecasting error with a regularization term. The estimation is made at each time stamp to adapt the forecast to short-term variations in solar activity.Peer ReviewedPostprint (published version

Generation of proxy GIM-TEC for extreme storms before the Era of GNSS observations

For the first time, we reconstructed global distribution of both the total electron content disturbance W index and TEC values for eight extreme storms (Dst < -250 nT) occurred before the epoch of GNSS observations in solar cycle 22. We created a model based on superposed epoch analysis of the training set of GIM-W maps of nine SC23 extreme storms. Global GIM-W index maps are calculated from 15-min UPC GIM-TEC (UQRG) as the logarithmic deviation of instantaneous TEC from the monthly median GIMMTEC empirical model. We introduced the storm phase metrics for main and recovery phases of the positive ionosphere disturbance (the WU-index), the negative disturbance (the WL-index) and the ring current (the Dst-index). The probabilistic forecasting model (Pmodel) for SC22 GIM-Wx maps is developed based on GIM-W maps of the SC23 training set. The storm phase distribution Fx for the eight SC22 extreme storms is calculated from the proxy time shift (lag) of peak WUmax and WLmin relative to Dstmin. Proxy GIM-TECx maps are calculated by adjusting the GIM-MTEC median to the GIM-Wx prediction. Validation of the technique based on data of UPC and JPL for four intense ionospheric storms showed a root-mean-square error less than 3 TECU. The proposed technique can be applied for both the past and future forecasting of GIM-W index and GIM-TEC maps.Peer ReviewedPostprint (published version

Method for forecasting ionospheric electron content fluctuations based on the optical flow algorithm

We present the optical flow algorithm for forecasting the rate of total electron content index (OFROTI). It consists of a method for predicting maps of rapid fluctuations of ionospheric electron content in terms of global navigation satellite system (GNSS) dual-frequency phase measurements of the rate of change of total electron content index (ROTI). The forecast is made in space and time, at horizons up to more than 6 h. These forecast maps will consist of the ROTI spatial distribution in the northern hemisphere above 45° latitude. The prediction method models the ROTI spatial distribution as a pseudoconservative flux, i.e., exploiting the inertia of the flux of ROTI to determine the future position. This idea is implemented as a modification of the optical flow image processing technique. The algorithm has been modified to deal with the nonconservation of the ROTI quantity in time. We show that the method can predict both, the local value of ROTI and also the regions with ROTI above a given level, better than the prediction using the current map as forecast, i.e., predicting by a current map from horizons of 15 min up to 6 h. The method was tested on 11 representative active and calm days during 2015 and 2018 from the multi-GNSS (GPS, GLONASS, Galileo, and Beidou) multifrequency measurements of more than 250 multi-GNSS receivers above 45°N latitude, including the high rate (1 Hz) measurements of Greenland geodetic network (GNET) network among the International GNSS Service network.This work is funded by ESA ITT “Forecasting Space Weather Impacts on Navigation Systems in the Arctic (Green-land Area)” Expro+, Activity No. 1000026374. The GNET GNSS observations from Greenland was kindly provided by The Danish Agency for Data Supply and Efficiency, in the Danish Ministry of Energy, Utilities and Climate, Copenhagen, DenmarkPeer ReviewedPostprint (author's final draft

On the detection of ionospheric waves, relationship with earthquakes and tsunamis

The research of this thesis addresses the detection and characterization of ionospheric waves and its application to traveling ionospheric disturbances (TIDs) induced by the natural events, such as earthquakes and tsunamis. The characterization is done from regional detrended Vertical Total Electron Content (VTEC) maps which are obtained from a set of Global Navigation Satellite System (GNSS) satellites. Note that from the mathematical and signal-processing point of view, the problem presents two key difficulties that are (a) the fact that ionospheric sampling is nonuniform, with different density of samples that somehow reflect the distribution of stations over the earth surface, and (b), that the estimation method can not introduce any constraints in the number of disturbances and their propagation parameters. In the first contribution of the thesis, we propose a method for detecting the number of simultaneous TIDs from a time series of high-pass-filtered VTEC maps and their parameters. The method, which we refer to as the Atomic Decomposition Detector of TIDs (ADDTID), is tested on the detrended VTEC map corresponding to a simulated realistic scenario from the dense GNSS network, Global Positioning System Earth Observation Network (GEONET) in Japan. The contribution consists of the detection of the exact number of independent TIDs from a nonuniform sampling of the ionospheric pierce points. The solution to the problem is set as the estimation of the representative perturbations from a dictionary of atoms that span a linear space of possible TIDs by means of a variation of the LASSO algorithm. These atoms consist of plane waves characterized by a wavelength, direction, and phase on a surface defined, the part of the ionosphere sounded by the GNSS observation. As the second contribution, we apply ADDTID on actual VTEC data to the GEONET network. We have studied the Medium Scale TIDs (MSTIDs) during the Spring Equinox day of 21 March 2011. The geophysical contribution is: (a) detection of circular MSTID waves compatible by time and center with a specific earthquake; (b) simultaneous superposition of two distinct MSTIDs, with almost the same azimuth; and (c) the presence of nighttime MSTIDs with velocities in the range 400-600 m/s. In the third contribution we provide a detailed characterization of the TIDs originated from the total solar eclipse of 21 August 2017, the shadow of which crossed the United States from the Pacific to the Atlantic ocean. This can be modeled in part as if the umbra and penumbra were moving cylinders that intersects with variable elevation angle a curved surface. The result of this is reflected in the time evolution of the TID wavelengths produced by the eclipse, which depend on the vertical angle of the sun with the surface of the earth, and also a double bow wave phenomenon, where the bow waves are generated in advance to the umbra. Finally, we detected a clear pattern of MSTIDs, which appeared in advance of the penumbra, which we could hypothesize as soliton waves associated with the bow wave. In the fourth contribution we characterized the MSTIDs generated during the Japan Tohoku earthquake of 11 March 2011. We found: (a) a confirmation of the performance of the algorithm in face of simultaneous multi-TID, the robustness to the curvature of the wave fronts of the perturbations and the accuracy of the estimated parameters. The results were double checked by the additional visual inspection from VTEC maps and keogram plots; (b) The detection of different wave fronts between the west and east MSTIDs around the epicenter, consistent in time and space with the post-earthquake tsunami; (c) The complete evolution of the circular MSTIDs driven by the tsunami during the GNSS observable area; (d) The detection of the fast and short circular TIDs related to the acoustic waves of earthquake.Esta tesis aborda la detección y caracterización de las ondas ionosféricas y su aplicación a las perturbaciones ionosféricas itinerantes (TID traveling ionospheric disturbances) inducidas por eventos naturales. La caracterización se realiza a partir de mapas regionales de Contenido Total Vertical de Electrones (VTEC) que se obtienen a partir de medidas de un conjunto de satélites del Sistema Navegación GNSS (Global Navigation Satellite System). Obsérvese que, desde el punto de vista matemático y de procesamiento de señales, el problema presenta dos dificultades: a) el hecho de que el muestreo ionosférico no es uniforme, con una densidad de muestras diferente que refleja de alguna manera la distribución de las estaciones sobre la superficie terrestre, y b) el hecho de que el método de estimación no puede introducir ninguna limitación en el número de perturbaciones y sus parámetros de propagación a detectar. En la primera contribución de la tesis, proponemos un método para detectar el número de TIDs simultáneas de una serie temporal de mapas VTEC filtrados por paso alto y sus parámetros. El método, al que denominamos como el Detector de Descomposición Atómica de TIDs (ADDTID), lo probamos con mapas VTEC, que corresponden a un escenario realista simulado en la red GEONET en Japón. La contribución consiste en la detección del número exacto de TIDs independientes a partir de un muestreo no uniforme de los IPPs de la ionosférica. La solución al problema se establece como la estimación de las perturbaciones representativas a partir de un diccionario de átomos que abarcan un espacio lineal de posibles TIDs mediante una variación del algoritmo LASSO. Estos átomos consisten en ondas planas caracterizadas por una longitud de onda, dirección y fase en una superficie definida. Como segunda contribución, aplicamos ADDTID a los datos VTEC a la red GEONET. Para probar el método, hemos estudiado los MSTIDs durante el día del Equinoccio de Primavera del 21 de marzo de 2011. La contribución geofísica es: (a) la detección de ondas circulares MSTID compatibles por tiempo y centro con un terremoto específico; (b) la superposición simultánea de dos MSTID distintos, con casi el mismo acimut; y (c) la presencia durante la noche de MSTID con velocidades en el rango de 400-600 m/s. En la tercera contribución presentamos una caracterización detallada de los TIDs originados por el eclipse solar total del 21 de agosto de 2017, cuya sombra atravesó los Estados Unidos desde el Pacífico hasta el Océano Atlántico. La evolución temporal de las TID producidas por el eclipse, que dependen del ángulo vertical del sol con la superficie de la tierra, y también aparece en un fenómeno de doble onda de choque. Finalmente, detectamos un patrón claro de MSTIDs, que aparecieron antes de la llegada de la penumbra, lo que podríamos hipotetizar como ondas de solitón asociadas con la onda de choque. En la cuarta contribución caracterizamos los MSTIDs generados durante el terremoto de Tohoku en Japón el 11 de marzo de 2011. Lo encontramos: a) una confirmación de la prestación del algoritmo frente al multi-TID simultáneas, la robustez frente a la curvatura de los frentes de onda de las perturbaciones y la precisión en la estimación de los parámetros. Los resultados se verificaron por duplicado mediante la inspección visual adicional de los mapas de VTEC y de los diagramas de keogramas; b) la detección de diferentes frentes de onda entre los MSTID del oeste y del este en torno al epicentro, coherentes en el tiempo y en el espacio con el maremoto posterior al terremoto; c) la evolución completa de las MSTID circulares que impulsó el maremoto durante el período observable en la zona de observación de los GNSS; y d) la detección de las MSTID circulares cortas y rápidas en el espacio en relación con las ondas acústicas asociadas con el terremoto.Postprint (published version

TEC forecasting based on manifold trajectories

In this paper, we present a method for forecasting the ionospheric Total Electron Content (TEC) distribution from the International GNSS Service’s Global Ionospheric Maps. The forecasting system gives an estimation of the value of the TEC distribution based on linear combination of previous TEC maps (i.e., a set of 2D arrays indexed by time), and the computation of a tangent subspace in a manifold associated to each map. The use of the tangent space to each map is justified because it allows modeling the possible distortions from one observation to the next as a trajectory on the tangent manifold of the map. The coefficients of the linear combination of the last observations along with the tangent space are estimated at each time stamp to minimize the mean square forecasting error with a regularization term. The estimation is made at each time stamp to adapt the forecast to short-term variations in solar activity.Peer Reviewe