The article proposes a straightforward Kalman filter-based method for computationally efficient ionospheric electron density multi-instrument imaging. The approach uses direct ionospheric measurements, such as ionosondes, and general physical assumptions to estimate the uncertainty associated with the previous reconstructed time step. Therefore the method does not require any electron density model of the ionosphere as a background. The uncertainty is represented by an inverse covariance matrix constructed with Gaussian Markov random fields, allowing the problem to be solved directly with relatively high resolution. The experiments utilize measurements from dense ground-based GNSS and low Earth orbit beacon satellite receiver networks as well as ionosondes. A synthetic simulation verification and real data validation with a specific European Incoherent Scatter Scientific Association incoherent scatter radar measurement campaign is carried out over Northern European sector. The method can be controlled using parameters with probabilistic and physically realistic interpretations that can be applied to both simulated and real-world data. The results show that the approach is feasible for near real-time regional ionospheric imaging. Especially, the method can be seen as an expansion to local profile measurements field of view, but with sufficient measurement coverage, it also provides information further away from the specific instrument.

Key Points

A Kalman filter application with Gaussian Markov random field priors enabling fast computation
No external ionospheric electron density model is used to generate the background mean or covariance
Verification with three-dimensional simulation model, as well as validation with incoherent scatter radars and ionosonde measurements

Plain Language Summary

The ionosphere is a region of the atmosphere with a large number of electrically charged particles. Earth's ionosphere extends typically from 100 to 1,000 km altitude. Electron density that is, the number of free electrons per volume is a commonly used quantity to describe the structure of the ionosphere. The electron density and its variations affects for example, satellite navigation and radio broadcasting. The ionosphere can be studied locally with a high degree of accuracy by different radar measurements such as ionosondes and incoherent scatter radars. Three-dimensional imaging of larger regions requires the use of ground-based satellite measurements. Despite today's numerous satellite systems and extensive receiver networks, electron density imaging is very difficult and therefore methods commonly use ionospheric models as a background. Hence, the imaging result is a compromise between the model and the satellite measurements. In this study, imaging is performed using local ionosonde measurements for eliminating the need for a background model. In addition, the use of so called Gaussian Markov random fields allows efficient computation of the resulting large numerical systems. The results obtained with both simulated and real measurements show that the approach is feasible for near real-time regional ionospheric imaging even with a modern laptop.

Open Research

Data Availability Statement

All the input, simulation and validation data used in the study (Norberg, 2022) are available at Zenodo via https://doi.org/10.5281/zenodo.6760141 as one data set with acknowledgments given below. The ground-based GNSS measurements are provided in an hdf5 file as geometry free combinations with satellite hardware biases removed. The daily GNSS data and the precise orbits are provided by International GNSS Service (IGS) and the International Association of Geodesy Reference Frame Sub-Commission for Europe Permanent GNSS Network (EUREF EPN) available from the EUREF EPN Regional Data Centre by Bundesamt für Kartografie und Geodäsie (https://igs.bkg.bund.de/). The dense GNSS networks in Finland and Sweden are provided by Geotrim (www.geotrim.fi) and Swepos https://swepos.lantmateriet.se. The data can be used for non-commercial scientific research. Daily multi-GNSS differential code bias estimates were obtained through NASA Crustal Dynamics Data Information System (CDDIS) https://cddis.nasa.gov/archive/gnss/products/bias/. The GUISDAP analyzed EISCAT incoherent scatter radar data was accessed via Madrigal Database at EISCAT (https://madrigal.eiscat.se/madrigal/) and EISCAT Dynasonde data via Dynasonde database (https://dynserv.eiscat.uit.no/DD/login.php) with simple registration. EISCAT is an international association supported by research organizations in China (CRIRP), Finland (SA), Japan (NIPR and ISEE), Norway (NFR), Sweden (VR), and the United Kingdom (UKRI). These data are the intellectual property of the EISCAT Scientific Association. They may be freely used for the purpose of illustration for teaching and for non-commercial scientific research, provided that the source is acknowledged and to the extent justified by the non-commercial purpose to be achieved. Substantial use of these data should be discussed at an early stage with knowledgeable scientists within the EISCAT Scientific Association (EISCAT's Headquarters, [email protected], can provide advice on suitable contacts) in order to clarify matters of use, calibration and potential co-authorship. Any further distribution of these data, including installation in any database, must be accompanied by this statement and subject to the same conditions of use. The Juliusruh Ionosonde data is owned by the Leibniz Institute of Atmospheric Physics Kuehlungsborn. An hdf5 file with independently solved (Vierinen et al., 2016) receiver DCBs used for comparison is included in the data set (Norberg, 2022). The GPS data used for DCB comparison and access through the Madrigal distributed data system are provided by the Massachusetts Institute of Technology (MIT) under support from US National Science Foundation Grant AGS-1242204. Data for TEC processing is provided from the following organizations: UNAVCO, Scripps Orbit and Permanent Array Center, Institut Geographique National, France, International GNSS Service, The Crustal Dynamics Data Information System (CDDIS), National Geodetic Survey, Instituto Brasileiro de Geografia e Estatística, RAMSAC CORS of Instituto Geográfico Nacional de la República Argentina, Arecibo Observatory, Low-Latitude Ionospheric Sensor Network (LISN), Topcon Positioning Systems, Inc., Canadian High Arctic Ionospheric Network, Centro di Ricerche Sismologiche, Système d’Observation du Niveau des Eaux Littorales (SONEL), RENAG: REseau NAtional GPS permanent, GeoNet—the official source of geological hazard information for New Zealand, GNSS Reference Networks, Finnish Meteorological Institute, and SWEPOS—Sweden. Access to these data is provided by madrigal network via: http://cedar.openmadrigal.org/. Version 2.2 of the Pyglow used for obtaining IRI 2012 data is developed and available at https://github.com/timduly4/pyglow. The International Reference Ionosphere (IRI) is an international project sponsored by the Committee on Space Research (COSPAR) and the International Union of Radio Science (URSI). GPSTk is sponsored by the Space and Geophysics Laboratory, within the Applied Research Laboratories at the University of Texas at Austin (ARL:UT). Version 8.0.0 of the GPSTk used for GNSS data processing is preserved and available via https://github.com/SGL-UT/GPSTk and developed openly at https://gitlab.com/sgl-ut/gnsstk-apps. Multifrontal Massively Parallel sparse direct Solver (MUMPS) used for matrix inversion is developed at http://mumps.enseeiht.fr. The R language MUMPS interface, RMUMPS, is developed openly at https://github.com/morispaa/rmumps. Besides the computation time, the results presented in the study do not dependent significantly on the third party software mentioned above or their specific versions, but other solvers could be used as well. In addition to all of the data providers and software developers mentioned above, we are grateful to the SuperMAG partners and members of the CASSIOPE/e-POP science team, especially the Coherent Electromagnetic Radiation tomography experiment (CER) for low Earth orbiting beacon radio transmissions.

Supporting Information

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Volume128, Issue1

January 2023

e2022JA030794

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2022JA030794-sup-0001-Supporting Information SI-S01.pdf100.2 KB	Supporting Information S1
2022JA030794-sup-0002-Movie SI-S01.mp431.4 MB	Movie S1
2022JA030794-sup-0003-Movie SI-S02.mp443.7 MB	Movie S2

Model-Free Approach for Regional Ionospheric Multi-Instrument Imaging

Abstract

Key Points

Plain Language Summary

Open Research

Data Availability Statement

Supporting Information

References

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References

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Model-Free Approach for Regional Ionospheric Multi-Instrument Imaging

Abstract

Key Points

Plain Language Summary

Open Research

Data Availability Statement

Supporting Information

References

Citing Literature

References

Related

Information

RESOURCES

PUBLICATION INFO