Artigo Acesso aberto Revisado por pares

Ionospheric imaging in Africa

2013; Wiley; Volume: 49; Issue: 1 Linguagem: Inglês

10.1002/2013rs005238

ISSN

1944-799X

Autores

Alex T. Chartier, J. Kinrade, Cathryn N. Mitchell, Julian Rose, D. R. Jackson, Pierre J. Cilliers, John Bosco Habarulema, Zama Katamzi, Lee-Anne Mckinnell, Tshimangadzo Merline Matamba, Ben Opperman, Nicholas Ssessanga, Nigussie Mezgebe Giday, Vumile Tyalimpi, Giorgiana De Franceschi, Vincenzo Romano, Carlo Scotto, Riccardo Notarpietro, Fabio Dovis, Eugene Avenant, Richard Wonnacott, E.O. Oyeyemi, A. Mahrous, Gizaw Mengistu Tsidu, Harvey Lekamisy, Joseph Olwendo, Patrick Sibanda, Tsegaye Kassa Gogie, A. B. Rabiu, Kees de Jong, A.O. Adewale,

Tópico(s)

Geophysics and Gravity Measurements

Resumo

Radio ScienceVolume 49, Issue 1 p. 19-27 Research ArticleOpen Access Ionospheric imaging in Africa Alex T. Chartier, Corresponding Author Alex T. Chartier Department of Electrical Engineering, University of Bath, Bath, UK Met Office, Exeter, UKCorresponding author: A. T. Chartier, Department of Electrical Engineering, University of Bath, Claverton, Bath, UK. ([email protected])Search for more papers by this authorJoe Kinrade, Joe Kinrade Department of Electrical Engineering, University of Bath, Bath, UKSearch for more papers by this authorCathryn N. Mitchell, Cathryn N. Mitchell Department of Electrical Engineering, University of Bath, Bath, UKSearch for more papers by this authorJulian A. R. Rose, Julian A. R. Rose Department of Electrical Engineering, University of Bath, Bath, UKSearch for more papers by this authorDavid R. Jackson, David R. Jackson Department of Electrical Engineering, University of Bath, Bath, UK Met Office, Exeter, UKSearch for more papers by this authorPierre Cilliers, Pierre Cilliers SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorJohn-Bosco Habarulema, John-Bosco Habarulema SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorZama Katamzi, Zama Katamzi SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorLee-Anne Mckinnell, Lee-Anne Mckinnell SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorTshimangadzo Matamba, Tshimangadzo Matamba SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorBen Opperman, Ben Opperman SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorNicholas Ssessanga, Nicholas Ssessanga SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorNigussie Mezgebe Giday, Nigussie Mezgebe Giday SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorVumile Tyalimpi, Vumile Tyalimpi SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorGiorgiana De Franceschi, Giorgiana De Franceschi Istituto Nazionale di Geofisica e Vulcanologia, Rome, ItalySearch for more papers by this authorVincenzo Romano, Vincenzo Romano Istituto Nazionale di Geofisica e Vulcanologia, Rome, ItalySearch for more papers by this authorCarlo Scotto, Carlo Scotto Istituto Nazionale di Geofisica e Vulcanologia, Rome, ItalySearch for more papers by this authorRiccardo Notarpietro, Riccardo Notarpietro Dipartimento di Elettronica, Politecnico di Torino, Torino, ItalySearch for more papers by this authorFabio Dovis, Fabio Dovis Dipartimento di Elettronica, Politecnico di Torino, Torino, ItalySearch for more papers by this authorEugene Avenant, Eugene Avenant SANSA Space Operations, Hartebeesthoek, South AfricaSearch for more papers by this authorRichard Wonnacott, Richard Wonnacott Chief Directorate: National Geospatial Information, Department of Rural Development and Land Reform, Cape Town, South AfricaSearch for more papers by this authorElijah Oyeyemi, Elijah Oyeyemi Department of Physics and Electronics, Rhodes University, Grahamstown, South AfricaSearch for more papers by this authorAyman Mahrous, Ayman Mahrous Space Weather Monitoring Center, Helwan University, Cairo, EgyptSearch for more papers by this authorGizaw Mengistu Tsidu, Gizaw Mengistu Tsidu Addis Ababa University, Addis Ababa, EthiopiaSearch for more papers by this authorHarvey Lekamisy, Harvey Lekamisy Madagascar Civil Aviation Authority, Antananarivo, MadagascarSearch for more papers by this authorJoseph Ouko Olwendo, Joseph Ouko Olwendo School of Pure and Applied Sciences, Pwani University, Mombasa, KenyaSearch for more papers by this authorPatrick Sibanda, Patrick Sibanda Department of Physics, University of Zambia, Lusaka, ZambiaSearch for more papers by this authorTsegaye Kassa Gogie, Tsegaye Kassa Gogie Bahir Dar University, Bahir Dar, EthiopiaSearch for more papers by this authorBabatunde Rabiu, Babatunde Rabiu Center for Atmospheric Research, Nigerian National Space Research and Development Agency, Abuja, NigeriaSearch for more papers by this authorKees De Jong, Kees De Jong Fugro Intersite B.V., Leidschendam, NetherlandsSearch for more papers by this authorAdekola Adewale, Adekola Adewale Department of Physics, University of Lagos, Akoka, NigeriaSearch for more papers by this author Alex T. Chartier, Corresponding Author Alex T. Chartier Department of Electrical Engineering, University of Bath, Bath, UK Met Office, Exeter, UKCorresponding author: A. T. Chartier, Department of Electrical Engineering, University of Bath, Claverton, Bath, UK. ([email protected])Search for more papers by this authorJoe Kinrade, Joe Kinrade Department of Electrical Engineering, University of Bath, Bath, UKSearch for more papers by this authorCathryn N. Mitchell, Cathryn N. Mitchell Department of Electrical Engineering, University of Bath, Bath, UKSearch for more papers by this authorJulian A. R. Rose, Julian A. R. Rose Department of Electrical Engineering, University of Bath, Bath, UKSearch for more papers by this authorDavid R. Jackson, David R. Jackson Department of Electrical Engineering, University of Bath, Bath, UK Met Office, Exeter, UKSearch for more papers by this authorPierre Cilliers, Pierre Cilliers SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorJohn-Bosco Habarulema, John-Bosco Habarulema SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorZama Katamzi, Zama Katamzi SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorLee-Anne Mckinnell, Lee-Anne Mckinnell SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorTshimangadzo Matamba, Tshimangadzo Matamba SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorBen Opperman, Ben Opperman SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorNicholas Ssessanga, Nicholas Ssessanga SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorNigussie Mezgebe Giday, Nigussie Mezgebe Giday SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorVumile Tyalimpi, Vumile Tyalimpi SANSA Space Science, Hermanus, South AfricaSearch for more papers by this authorGiorgiana De Franceschi, Giorgiana De Franceschi Istituto Nazionale di Geofisica e Vulcanologia, Rome, ItalySearch for more papers by this authorVincenzo Romano, Vincenzo Romano Istituto Nazionale di Geofisica e Vulcanologia, Rome, ItalySearch for more papers by this authorCarlo Scotto, Carlo Scotto Istituto Nazionale di Geofisica e Vulcanologia, Rome, ItalySearch for more papers by this authorRiccardo Notarpietro, Riccardo Notarpietro Dipartimento di Elettronica, Politecnico di Torino, Torino, ItalySearch for more papers by this authorFabio Dovis, Fabio Dovis Dipartimento di Elettronica, Politecnico di Torino, Torino, ItalySearch for more papers by this authorEugene Avenant, Eugene Avenant SANSA Space Operations, Hartebeesthoek, South AfricaSearch for more papers by this authorRichard Wonnacott, Richard Wonnacott Chief Directorate: National Geospatial Information, Department of Rural Development and Land Reform, Cape Town, South AfricaSearch for more papers by this authorElijah Oyeyemi, Elijah Oyeyemi Department of Physics and Electronics, Rhodes University, Grahamstown, South AfricaSearch for more papers by this authorAyman Mahrous, Ayman Mahrous Space Weather Monitoring Center, Helwan University, Cairo, EgyptSearch for more papers by this authorGizaw Mengistu Tsidu, Gizaw Mengistu Tsidu Addis Ababa University, Addis Ababa, EthiopiaSearch for more papers by this authorHarvey Lekamisy, Harvey Lekamisy Madagascar Civil Aviation Authority, Antananarivo, MadagascarSearch for more papers by this authorJoseph Ouko Olwendo, Joseph Ouko Olwendo School of Pure and Applied Sciences, Pwani University, Mombasa, KenyaSearch for more papers by this authorPatrick Sibanda, Patrick Sibanda Department of Physics, University of Zambia, Lusaka, ZambiaSearch for more papers by this authorTsegaye Kassa Gogie, Tsegaye Kassa Gogie Bahir Dar University, Bahir Dar, EthiopiaSearch for more papers by this authorBabatunde Rabiu, Babatunde Rabiu Center for Atmospheric Research, Nigerian National Space Research and Development Agency, Abuja, NigeriaSearch for more papers by this authorKees De Jong, Kees De Jong Fugro Intersite B.V., Leidschendam, NetherlandsSearch for more papers by this authorAdekola Adewale, Adekola Adewale Department of Physics, University of Lagos, Akoka, NigeriaSearch for more papers by this author First published: 11 December 2013 https://doi.org/10.1002/2013RS005238Citations: 12 The copyright line for this article was changed on 18 September 2014. AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract [1] Accurate ionospheric specification is necessary for improving human activities such as radar detection, navigation, and Earth observation. This is of particular importance in Africa, where strong plasma density gradients exist due to the equatorial ionization anomaly. In this paper the accuracy of three-dimensional ionospheric images is assessed over a 2 week test period (2–16 December 2012). These images are produced using differential Global Positioning System (GPS) slant total electron content observations and a time-dependent tomography algorithm. The test period is selected to coincide with a period of increased GPS data availability from the African Geodetic Reference Frame (AFREF) project. A simulation approach that includes the addition of realistic errors is employed in order to provide a ground truth. Results show that the inclusion of observations from the AFREF archive significantly reduces ionospheric specification errors across the African sector, especially in regions that are poorly served by the permanent network of GPS receivers. The permanent network could be improved by adding extra sites and by reducing the number of service outages that affect the existing sites. Key Points Ionospheric image quality in Africa is assessed Simulated and real data are both used An extended receiver network greatly improves accuracy 1 Introduction [2] Human activities such as radar detection and satellite positioning are affected by ionospheric electron densities. Ionospheric imaging could be used to estimate the effects on these activities in the African sector. The work presented here utilizes a simulation approach to determine the accuracy of tomographic images of the ionosphere. This approach allows application developers to quantify the benefits of including observations from sites that are not currently operational. Real images are also presented and analyzed. Ionospheric Tomography [3] Global Positioning System (GPS) ionospheric tomography techniques invert observations of relative or calibrated slant total electron content (TEC) from dual-frequency GPS receivers to produce three-dimensional, time-dependent images of electron density. The technique used here, known as the Multi-Instrument Data Analysis System (MIDAS), is based on an algorithm by Mitchell and Spencer [2003] and developed by Spencer and Mitchell [2007]. The current version of the algorithm is described in detail in Chartier et al. [2012a]. MIDAS solves for three-dimensional electron densities at multiple times from differential phase measurements of slant TEC using a vertical basis function decomposition and a horizontal smoothing function. When relative slant TEC observations (from differential phase measurements) are used, there is no need to calculate the hardware biases because those biases only affect pseudorange measurements of TEC. Allain and Mitchell [2009] showed that a real-time version of MIDAS could improve single-frequency GPS position estimates by up to 25 m at midlatitudes during solar maximum. Alternative ionospheric imaging techniques have been developed by Bust et al. [2000, 2004], Schunk et al. [2004], Mandrake et al. [2005], and Angling and Jackson-Booth [2011]. Andreeva et al. [2000] studied the equatorial ionization anomaly using an ionospheric tomography algorithm. Ionospheric Observations [4] In common with other ionospheric imaging techniques, MIDAS depends on good data coverage and utilizes certain assumptions to fill data gaps. Ionospheric imaging in the African sector presents a special challenge since there is a large gap in GPS receiver coverage in the Sahara (see Figure 1). The observations used in this study are provided by three networks: the International Global Navigation Satellite Systems (GNSS) Survey (IGS), the University Navstar Corporation (UNAVCO) and the African Geodetic Reference Frame (AFREF). The IGS network is described by Dow et al. [2009]. Figure 1Open in figure viewerPowerPoint The map shows working dual-frequency GPS receiver sites on the IGS network in blue and additional sites from the AFREF and UNAVCO networks in red. Only sites that produced usable observations in the period 2–16 December 2012 are shown here. [5] Figure 1 shows that operationally available sites (those provided by the IGS and those from UNAVCO) cover northern and southern Africa quite well, but there are less data available between 15°N and 25°N. The AFREF project is primarily aimed at unifying geodetic reference frames for Africa, but it also recognizes other applications of GNSS signals, such as for ionospheric imaging. By including data from these receivers in simulated inversions, it is possible to assess the impact of observations that come from geographically feasible locations. A comparison can be made between the quality of ionospheric reconstructions from existing data and the improvements that can arise from including additional receiver stations. Ionospheric Models [6] The work described in this paper relies on realistic simulations of ionospheric electron density to serve as a ground truth. The latest version of International Reference Ionosphere (IRI), IRI-2012, is chosen for this purpose. The observational noise that is to be expected from subgrid-scale structures is dealt with separately (see section 2.3). IRI-2012 is an empirical model of the ionosphere based on a wide range of ground and space data, including incoherent scatter radars and topside sounders [Bilitza et al., 2011]. It is the result of collaboration between the Committee on Space Research and the International Union of Radio Science that began in 1969. IRI estimates the monthly median electron density, ionized gas composition, and temperature in the altitude range 50–1500 km. 2 Method [7] The quality of ionospheric reconstructions is difficult to assess without an independent ground truth. In this experiment, we use a modeled ionosphere from IRI-2012 as a ground truth. Simulated GPS TEC observations through this modeled ionosphere are created and used in MIDAS inversions. As well as allowing for comparison of the images with the ground, this approach allows us to quantify the benefits of including observations from additional sites that are not currently operationally available. A similar approach was used by Dear and Mitchell [2006] in Europe and by Zapfe et al. [2006] in South America. Differences between the model and the reconstructed images are then due to a lack of observations or due to poor assumptions about the nature of the solution. While the MIDAS inversion technique can use IRI to create basis functions and to provide an initial guess at the solution, those options are disabled for this experiment. Instead, we use two basis functions derived from Chapman's equations and a 4° horizontal grid. In addition to assuming that the ionosphere can be adequately represented by these constraints, a regularization condition is applied that favors solutions with zero second derivative in each horizontal direction and in time. These assumptions are necessary to obtain a unique solution and to cover data gaps, but it is noted that the assumptions could prove problematic if they are not appropriate for a specific ionosphere. The selection of IRI-2012 as the "truth" ionosphere might artificially enhance the performance of the imaging algorithm because IRI-2012 is smoother than the real ionosphere, and our algorithm favors smooth solutions. This problem is addressed by adding realistic noise caused by subgrid-level structures to the observations. However, scintillation is not modeled here. Simulating the Ionosphere [8] IRI-2012 is used to create three-dimensional fields of electron density values on the same 4° grid that will be used for the reconstructions. MIDAS uses observations from a time window around the inversion, so it is necessary to simulate the ionosphere for multiple times. In this case, we use a time window of 7 h and 30 min with a time step of 30 min. The result is that for each inversion, 15 IRI simulations are created at 30 min intervals. The resulting IRI electron density values are arranged into a simulated state vector, xIRI. Simulating a Receiver Network [9] In order to find the upper limit of imaging accuracy possible using the chosen grid for the MIDAS algorithm, it is necessary to simulate a network of receivers that would provide adequate observation coverage. This is achieved by creating a regularly spaced list of coordinates to represent fictitious receivers at 8° intervals in latitude and longitude. This receiver spacing was chosen because it was found that increasing receiver coverage above 8° spacing made almost no difference to image accuracy. This list of coordinates is combined with the known position of the GPS satellites to find the trajectories of the rays that would be observed by the simulated receiver network. Real receiver networks can be also used in the simulation approach, with the added advantage that data outages can be taken account of. This is described in the next section. Simulating Observations [10] As already noted, it is necessary to create TEC "observations" of the simulated ionosphere in order to produce reconstructed images. This is achieved using an observation operator, H, that is based on the trajectories of real or simulated observations. H describes the raypath contributions of the observations to the grid. H is created by tracing raypaths from the GPS satellites to the receivers at the times when data are received. In order to create a vector of simulated observations, zIRI, we multiply the simulated state vector by the observation operator, i.e., (1) [11] We assume that real GPS differential phase observations of slant TEC do not contain significant errors, although they do contain cycle slips. It is possible that the observations are not representative of grid-scale structures—there could be significant subgrid-level "noise" in the real ionosphere. This could happen if structures exist in the ionosphere that are too small to image using the specified resolution. Our simulated ionosphere, IRI-2012, will not have these subgrid-scale structures because it is defined on the same grid that will be used in the inversion. The simulated ionosphere is also far smoother than the real ionosphere. It is important to include realistic errors of representativeness in the simulation so that the inversion accuracy is not artificially enhanced. This is achieved by creating images, xREAL, of the real electron density distribution using real observations of slant TEC, zREAL, and then calculating the residuals, r, of the observations from the images, i.e., (2) [12] These residuals are added to the simulated observations of slant TEC in order to take account of the effects of subgrid-level structures on image accuracy. Reconstructions Using Simulated Observations [13] The simulated observations are inverted in order to reconstruct the simulated ionosphere. The normal MIDAS inversion procedure is followed. First, the problem is mapped from electron density space to basis function space. A mapping function, M, is used to make the transformation. Then a regularization condition, R, is applied that penalizes solutions that contain nonzero second derivatives of electron density in horizontal space and in time. There is no regularization of the vertical profile. In practice, a weighting term, λ, has to be included in order to balance the effects of the measurements and the regularization on the solution. Within MIDAS, a heuristic choice is made to define the regularization weighting as (3) [14] Finally, the constrained problem is inverted to obtain a solution, xRETRIEVED, for all the times in the time window, i.e., (4) [15] The central slice in time is selected as the final image. The retrieved solution, xRETRIEVED, is compared with the original ionospheric simulation, xIRI, in order to determine the accuracy of the imaging technique, given the available data. [16] A 2 week period of the recent AFREF campaign provided a great deal of extra GPS coverage in the African sector (see Figure 1). This provides the opportunity to contrast the image quality possible using the existing IGS network with the image quality that an extended network could provide. The procedure outlined above is run twice: once using just the available IGS sites and a second time supplementing this with the sites available through UNAVCO and AFREF. Simulation inversions are performed for the maximum AFREF data availability period of 2–16 December 2012. Differences between the two sets of images show the improvements in accuracy that can be achieved by using additional receivers. 3 Results [17] Following the procedure described in section 2, three sets of simulated inversions were produced for the maximum AFREF data availability period (2–16 December 2012). The first set of images is based on the simulated, regularly spaced receiver network. These results provide an estimate of the upper limit of imaging accuracy achievable using the MIDAS algorithm at a 4° grid resolution under ideal conditions. The other two sets of images are created to determine the imaging accuracy achievable using real GPS receiver networks. One set of images was based on simulated observations at the locations of the IGS receivers, while the other set was based on all the available receivers. In each case, images were produced every 30 min throughout the test period. Imaging Under Optimal Conditions [18] Although insufficient observation coverage is likely to be the primary source of error in ionospheric images, it is possible that inherent properties of the imaging technique also limit accuracy. The results presented in this section demonstrate the performance of the imaging technique when provided with high-density (8° spaced) and uniform GPS receiver coverage. One hundred receivers are used in total. An example of the model truth and the image obtained from this high-density simulated network is shown in Figure 2. Figure 2Open in figure viewerPowerPoint (left) An IRI modeled truth. (right) A reconstructed image based on observations of the modeled truth from a fictitious receiver network (shown in white). The model and reconstructed image are from 12:00 UT on 7 December 2012. [19] Images such as the one in Figure 2 are produced at 30 min intervals over the period 2–16 December 2012. In order to assess the errors of the images, differences between the reconstructed images and the modeled truth are calculated over the whole period. The root-mean-square (RMS) errors of the images from the fictitious receiver network are shown in Figure 3. Figure 3Open in figure viewerPowerPoint The RMS errors of reconstructions based on simulated observations from a dense network of simulated receivers are shown here. The simulated receiver sites are shown in white. The IRI simulations that the observations are based on are used as the ground truth here. The RMS errors are based on hourly reconstructions from the 2 week test period (2–16 December 2012). [20] The results in Figure 3 show that relatively small errors can be achieved when a dense network of receivers is available—errors range from 0 to 5 TECU (TEC unit, 1 TECU = 1016 el m−2) here. Errors are clearly highest at the locations of the two bands of increased ionization created by the Appleton anomaly (around 10°S–0° and 15°N–20°N). As well as the higher TEC values present here, the TEC gradients seen in this region are likely to contribute to these higher errors. The imaging technique includes a regularization condition that favors zero second derivatives in the horizontal directions—a condition that is clearly broken as we move over the Appleton anomaly in a longitudinal direction. Data Coverage [21] In order to illustrate the typical data coverage available for each set of images, a pair of case studies are shown in Figure 4. The 300 km pierce points of all the rays available for use in each image are shown. These rays are collected at 30 min intervals over a 7.5 h time window. The case study shows data from 00:00 to 07:30 UT on 3 December 2012. Figure 4Open in figure viewerPowerPoint The GPS raypath coverage obtained from (right) the IGS network (blue) and (left) the full IGS, AFREF, and UNAVCO network (red) during a typical imaging period (00:00–07:30 UT on 3 December 2012) is shown here. Plotted in black are 300 km raypath pierce points. The observations represented here are used in the images at 04:00 UT on 3 December 2012. [22] Figure 4 shows that the full network provides far more raypath coverage than the IGS network alone. The IGS network has only isolated patches of coverage during the test period, while the full network only has a few large gaps. There are numerous redundant receivers in the full network—a similar level of coverage could be achieved with far fewer receivers, but such a network would be vulnerable to station outages. Case Studies [23] It is useful to examine the images from the two simulations alongside the original IRI simulations in order to understand how the structures in the ionosphere affect the resulting image accuracy. Figure 5 shows a series of case studies that depict the way the image quality varies depending on the ionospheric state. The examples were selected to show a range of different features that occur at different times of day. Figure 5Open in figure viewerPowerPoint (left) The IRI simulations, (middle) the reconstructions based on all the available data, and (right) the reconstructions based on just the IGS data. (a) For 22:00 UT on 2 December 2012. (b) For 17:00 UT on 3 December 2012. (c) For 12:00 UT on 7 December 2012. The GPS receiver sites used to make each set of reconstructions are shown in white. [24] All the case studies shown in the right column in Figure 5, based on just IGS data, overestimate the IRI simulated truth in the left column more than the images based on all the data. However, the errors are generally overestimates in both cases. A nighttime case study is not included here because the lack of large-scale ionospheric structuring and lower electron densities at night make imaging much easier. [25] The different case studies give an insight into the reasons for the overestimation. Figure 5a shows a significant overestimation of TEC in the western region of the IGS reconstruction. This is caused by the regularization condition, which extrapolates the gradients observed in the north and east of the image. The lack of data in the western region allows the TEC values to continue increasing until the edge of the image. This does not occur in the reconstruction based on all the available data because there are numerous active receiver sites in the western part of the image. The lack of data could equally have resulted in artificially low TEC values, but the distribution of receiver sites in this case means that TEC generally increases from the observed to the unobserved parts of the grid. This positive gradient causes the artificial enhancements observed. [26] The IGS-only reconstruction in Figure 5b has the western TEC enhancement most clearly shown in Figure 5a, but Figure 5b also contains a more unusual artifact. In this case, the IGS-only reconstruction has underestimated the northern band of ionization caused by the equatorial ionization anomaly in the northeastern sector. It appears that the sites above and below this phenomenon have measured only small positive gradients toward the band of ionization, and therefore, the interpolation has resulted in an underestimate. The reconstruction with all the available data shows that it is possible to image this phenomenon accurately when two east African receivers are present. [27] In Figure 5c and, to a lesser extent, Figure 5b, both reconstructed images overestimate the TEC values of the IRI truth image. The overestimation is caused by the regularization condition, which extrapolates a constant gradient across data-sparse regions. This is evident in the west of the images, where there are few observations available. RMS Errors [28] To measure the accuracy of the images, we calculate the differences between the vertical TEC from the images and the vertical TEC from the simulations that the images are based on. Spatially distributed root-mean-square (RMS) errors are calculated based on the errors of the entire period (2–16 December 2012) and plotted in Figure 6. Figure 6Open in figure viewerPowerPoin

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