An accurate and efficient algorithm for Faraday rotation corrections for spaceborne microwave radiometers

The ionosphere is a highly dynamic medium that exhibits weather disturbances at all latitudes, longitudes, and altitudes, and these disturbances can have detrimental effects on both military and civilian systems. In an effort to mitigate the adverse effects, we are developing a physics‐based data assimilation model of the ionosphere and neutral atmosphere called the Global Assimilation of Ionospheric Measurements (GAIM). GAIM will use a physics‐based ionosphere‐plasmasphere model and a Kalman filter as a basis for assimilating a diverse set of real‐time (or near real‐time) measurements. Some of the data to be assimilated include in situ density measurements from satellites, ionosonde electron density profiles, occultation data, ground‐based GPS total electron contents (TECs), two‐dimensional ionospheric density distributions from tomography chains, and line‐of‐sight UV emissions from selected satellites. When completed, GAIM will provide specifications and forecasts on a spatial grid that can be global, regional, or local. The primary output of GAIM will be a continuous reconstruction of the three‐dimensional electron density distribution from 90 km to geosynchronous altitude (35,000 km). GAIM also outputs auxiliary parameters, including NmF2, hmF2, NmE, hmE, and slant and vertical TEC. Furthermore, GAIM provides global distributions for the ionospheric drivers (neutral winds and densities, magnetospheric and equatorial electric fields, and electron precipitation patterns). In its specification mode, GAIM yields quantitative estimates for the accuracy of the reconstructed ionospheric densities.

Longitudinal behaviors of the IRI-B parameters of the equatorial electron density profiles retrieved from FORMOSAT-3/COSMIC radio occultation measurements

A successful ionospheric electron density model assimilates relevant data for determination of its driving parameters. We process about two hours worth of two‐frequency GPS ground‐receiver data from five satellites in order to separate the least squares solution of up to four driving parameters of the electron density profile (EDP) model from the solution of four relative (between satellites) differential hardware biases. The EDP model we use is part of the Ionosphere and Troposphere Raytrace Model (ITRAY), which is our upgrade of the Raytrace/Ionospheric Conductivity and Electron Density model (ICED)‐Bent‐Gallagher (RIBG) model. We use the Westford GPS receiver in Massachusetts to update the EDP model, which we then use to predict EDP distributions at nearby Millstone Hill for comparison with ground truth incoherent‐scatter radar and Digisonde data. We find that a simple procedure often works well when the model time dependence is correct, but we find that forcing the ionospheric model to more closely fit GPS data actually degrades ionospheric specification in the F layer region. We suggest a data diversification remedy.

China Seismo‐Electromagnetic Satellite (CSES) was successfully launched in February 2018. About 280 thousand ionospheric radio occultation (RO) electron density profiles (EDP) have been accumulated till the end of 2020. The CSES is a Sun‐synchronous orbit satellite with descending and ascending nodes around 14:00 and 02:00 LT, respectively, at the height of 507 km. Thus, most of the RO EDP concentrate on these two local time bins. First, we constructed empirical NmF2, hmF2, and Hm models at two local time windows 14:00 and 02:00 LT, respectively. The three models describe that NmF2, hmF2, and Hm vary with solar activity, season, longitude, and latitude. Through the comparison with CSES observations, the NmF2, hmF2, and Hm models could reproduce the physical characteristics rather well. Then, according to Chapman profile function, a EDP model was reconstructed based on the NmF2, hmF2, and Hm models, named CSES_Ne‐Profile Model. To evaluate the model performance, we simulated the COSMIC‐2 observations by CSES_Ne‐Profile Model and international reference ionosphere (IRI) model respectively. The results show that CSES_Ne‐Profile Model precedes the IRI model. Additionally, our model captures the merging phenomenon of the two peaks of equatorial ionospheric anomaly, which is missed by IRI. Further, CSES_NePrf model is a useful tool to provide the quiet background for case studies and joint studies with other payloads onboard CSES.

• Lightning waveforms reliably yield estimates for D-region electron density profiles when analysed. Lightning waveforms in the low frequency (LF; 30–300 kHz) and the very low frequency (VLF; 3–30 kHz) bands can be exploited to produce data-driven ionospheric D-region electron density profile (EDP) estimates with significantly higher spatial and temporal coverage than previously available. The lightning waveforms used in this paper are signals detected in the LF/VLF of negative cloud-to-ground lightning by the Earth Networks Total Lightning Detection Network. Each waveform contains a ground wave and a time-delayed ionospheric reflection. The time delay between the ground wave and ionospheric reflection has previously been used to estimate a single specular reflection altitude, where LF/VLF emissions are reflected by the ionosphere. Here, we expand upon previous methods to include filtering and spectral analysis, and account for oblique propagation to produce higher-order estimates for reflection altitudes and corresponding electron densities. Once estimated, reflection altitudes and corresponding electron densities can be used to derive parameters β and h ′, which define an EDP for the D-region. In this study, the lightning waveform (LW) analysis is demonstrated using a single representative 24-h dataset over the Southeast United States, and then extended to a total of 10 separate datasets with varying locations and ionospheric conditions. The LW-derived D-region EDPs are in agreement with predictions made by the Faraday International Reference Ionosphere model, and the LW EDPs β and h ′ values are consistent with previous LF/VLF-derived estimates.

Predicting the behaviour of the Earth’s ionosphere is crucial for the ground-based and spaceborne technologies that rely on it. This paper presents a novel way of inferring ionospheric electron density profiles and electron temperature profiles using machine learning. The analysis is based on the Nearest Neighbour (NNB) and Radial Basis Function (RBF) regression models. Synthetic data sets used to train and validate these two inference models are constructed using the International Reference Ionosphere (IRI 2020) model with randomly chosen years (1987–2022), months (1–12), days (1–31), latitudes (−60 to 60°), longitudes (0, 360°), and times (0–23 h), at altitudes ranging from 95 to 600 km. The NNB and RBF models use the constructed ionosonde-like profiles to infer complete ISR-like profiles. The results show that the inference of ionospheric electron density profiles is better with the NNB model than with the RBF model, while the RBF model is better at inferring the electron temperature profiles. A major and unexpected finding of this research is the ability of the two models to infer full electron temperature profiles that are not provided by ionosondes using the same truncated electron density data set used to infer electron density profiles. NNB and RBF models generally over- or underestimate the inferred electron density and electron temperature values, especially at higher altitudes, but they tend to produce good matches at lower altitudes. Additionally, maximum absolute relative errors for electron density and temperature inferences are found at higher altitudes for both NNB and RBF models.

<p>Ionosphere is one of the main errors in the signal propagation of global navigation system satellite (GNSS), and it is also the key issue of space weather. The International Reference Ionosphere (IRI) is the most important empirical model described the ionospheric characteristics, and it provides the monthly averages of electron densities and vertical total electron content (VTEC) in the altitude range of 50km-2000km. The IRI-2016 model is the latest version. But some studies showed that the accuracy of the IRI model is not high enough in China due to the use of fewer data sources. This paper will assess the performance of IRI-2016 model in China, and a modified IRI 2016 model by adjusting the driving parameters IG and RZ index of IRI2016 model with GNSS TEC data are also investigated. In this contribution, GNSS data from the Crustal Movement Observation Network of China (CMONC) are used to estimate TEC values, and the ionosonde data from three stations are used as references for the ionospheric electron densities. Three ionosonde stations are located at Beijing (BP440, 40.3°N/116.2°E), Wuhan (WU430, 30.5°N/114.4°E) and Sanya (SA418, 18.3°N/ 109.6°E). The above data respectively cover a period of 6 days in the high year (2015) and low year (2019) of solar activity.</p><p>The study shows that the biggest reason for the difference (DTEC) between GPS-TEC and IRI2016-TEC in China is that the poor estimation of NmF2 and hmF2 by IRI model, and the driving parameters IG and RZ index of IRI2016 can be updated by constraining DTEC. Finally, the performance of the modified IRI-2016 model is improved by the updated IG and RZ indexes as the short-term driving values of ionospheric parameters. The analysis show that the modified IRI-2016 model is more accurate at estimating both the TEC and the electron density profile than the original model.</p>

For the most accurate ray-tracing in an anisotropic ionosphere with realistic 3D electron density gradients, it is found that the ionosphere model should be a continuous function of the spatial co-ordinates and thus also the electron density. The spatial derivatives of the refractive index should also be continuous for first, second and higher order derivatives. To perform ray-tracing in a 3D ionosphere model such as International Reference Ionosphere (IRI), the vertical profile must first be accurately fitted by some analytical basis functions. Unlike parabolic or quasi-parabolic basis functions, exponential functions, taken to some exponent n, make a good choice because they and their derivatives are always continuous. These are then used to match the vertical electron density profile of an IRI modelled ionosphere. To accomplish this, a 3D fit to the IRI ionosphere is determined over the desired area of latitude and longitude in which the ray-tracing is to be performed. Results are presented for transionospheric paths through the equatorial ionosphere where the large electron density gradients associated with the equatorial anomaly cause refraction and significant differences in time delay of transionospheric signals. These are then presented for different elevation angles of propagation from 10 to 90 degrees and show the significant variation and complex effects arising from the latitudinal electron density gradients.

An improved method for identifying sporadic E (Es) layer properties from radio occultation (RO) electron density profiles (EDPs) is presented. The data used are sourced from COSMIC-1 RO EDPs collected between 2006 and 2019, which cover altitudes from 75 to 145 km. Initially, we evaluate the reliability of EDPs using the International Reference Ionosphere 2016 (IRI-2016) model and select only those profiles with a reliability score of 0.6 or higher (on a scale up to 1) for further analysis. Preliminary Es layer inversion results are obtained and validated against electron density data derived from ionosonde fbEs measurements, demonstrating a linear correlation with a coefficient of 0.72 and a mean absolute percentage error of 36.08%. Further verification using RO S4max data shows that this research method achieved an accuracy of 85.3% in identifying Es events. We perform a detailed analysis of Es layer relative occurrence rates, intensity, and thickness. The Es intensity is expressed by NmμEs (the layer’s maximum electron density (Nm) corresponding to the metal (μ) ion), which is estimated from the measured layer peak electron density NmEs by subtracting the ambient E region electron density NeE(hEs) at the height of the layer’s peak hEs, computed from the IRI-2016 model. Our findings reveal that Es layers predominantly occur in mid-latitude regions during summer, with average intensities between 5×104and8×104el/cm3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5\ imes {10}^{4 }\ ext{ and }8\ imes {10}^{4 }\ ext{el}/{\ ext{cm}}^{3}$$\\end{document}. The most likely thickness of Es layers is approximately 1.4 km. Additionally, the present study shows that because NeE(hEs) increases during daytime, which leads to increases in NmEs, confirming that NmμEs is the proper parameter for assessing the Es layer intensity, in line with what is suggested by Haldoupis et al. (Haldoupis et al., J Atmos Sol Terr Phys 206:105327, 2020).Graphical

Global Positioning System (GPS) data for phase delay differential between Ll and L2 frequencies are analyzed by a model in which the combined effect of hardware and phase ambiguity terms is represented by a constant for each receiver‐satellite path and the ionospheric contribution is represented by the RIBG model (ray trace through the combined ICED (ionospheric conductivity and electron density), Bent, and Gallagher ionospheric models). RIBG contains a detailed global empirical climatological ionospheric model of the electron density versus height profile (EDP) from 80 km up to the plasmapause, which is combined with a full three‐dimensional ray trace propagation model. Discrete inverse theory (DIT) is used to fit the driving parameters of RIBG to about 2 hours worth of data from a single GPS receiver at various geographical locations. Validity is demonstrated by the ability of the GPS‐updated RIBG model to predict independent measurements of (1) vertical total electron content (TEC) over the ocean out to substantial distances from a GPS receiver, often in excess of 2000 km at midlatitudes, and (2) the electron density versus height profile (EDP). Performance variation with magnetic latitude is noted. Flexibility in RIBG to adjust different driving parameters for different parts of the EDP, in order to obtain a best fit of GPS data, benefits the EDP prediction. Implications of this approach for GPS navigation and other radio system applications are discussed.

Abstract. The influence of atomic oxygen concentration on the height distribution of the main positive and negative ions and on electron density in the mesosphere is studied for the conditions prevailing during the solar proton event on 17 January 2005. It is shown by numerical modeling that the electron and ion density profiles are strongly dependent on the choice of the atomic oxygen profile. Experimental measurements of the electron density are used as the criterion for choosing the atomic oxygen profile in the mesosphere. With the help of modeling, the atomic oxygen profile in the daytime in the winter mesosphere is found to lead to a model electron density profile best matching the electron density profile obtained experimentally. As a result, with the help of modeling, we find the atomic oxygen profiles at various solar zenith angles in the winter mesosphere which lead to model electron density profiles matching the electron density profiles obtained experimentally. Alteration of the atomic oxygen concentration leads to a redistribution of the abundance of both positive and negative ion constituents, with changes in their total concentrations and transition heights. In consequence this results in changes of the electron density and effective recombination coefficient. For conditions of low concentration of atomic oxygen (during a solar proton event), the formation of cluster ions is the key process determining electron and ion densities at altitudes up to 77 km. The complex negative CO3− ion is formed up to about 74 km and the final NO3− ion, which is stable in relation to the atomic oxygen, is the dominant negative ion up to 74 km. As a result the transition heights between cluster ions and molecular ions and between negative ions and electron density are located at 77 km and 66 km, respectively.

To generate high-quality reconstructions of ionospheric electron density (IED), we propose an extended simultaneous algebraic reconstruction technique (ESART). The ESART method distributes the discrepancy between the actual GNSS TEC and the calculated TEC among the ray–voxels based on the contribution of voxels to GNSS TEC, rather than the ratio of the length of ray–voxel intersection to the sum of the lengths of all ray–voxel intersections, as is adopted by conventional methods. The feasibility of the ESART method for reconstructing the IED under different levels of geomagnetic activities is addressed. Additionally, a preliminary experiment is performed using the reconstructed IED profiles and comparing them with ionosonde measurements, which provide direct observations of electron density. The root mean square errors (RMSE) and absolute errors of the ESART method, the simultaneous algebraic reconstruction technique (SART) method, and the International Reference Ionosphere (IRI) 2016 model are calculated to evaluate the effectiveness of the proposed method. Compared to the conventional SART method of ionospheric tomography and the IRI-2016 model, the reconstructed IED profiles obtained using the ESART method are in better agreement with the electron density obtained from the ionosondes, especially for the peak electron densities (NmF2). In addition, a case study of an intense geomagnetic storm on 17–19 March 2015 shows that the spatial and temporal features of storm-related ionospheric disturbances can be more clearly depicted using the ESART method than with the SART method.

High‐frequency (HF) direction‐finding (DF) systems measure the angles of arrival of signals at selected frequencies. With this information, ray tracing can accurately determine the location of the HF transmitters if the three‐dimensional (3‐D) electron density (Ne) distribution between the DF site and the transmitters is known. The usual approach is to use an ionospheric model like the International Reference Ionosphere (IRI) as a proxy for the density distribution. We describe a more realistic approach developed in cooperation with Codem Systems in Merrimack, New Hampshire. A collocated digisonde at the DF site measures the vertical electron density profile and the local ionospheric tilt, providing, in real time, the inputs for the construction of the 3‐D Ne distribution. The vertical profile is automatically obtained from the Automated Real Time Ionogram Scaler with True Height (ARTIST)‐scaled ionogram and the local tilt from the sky maps recorded after each ionogram. The characteristics of each layer, for example, critical frequencies and peak heights, are expressed as a function of latitude λ and longitude Ψ. In the neighborhood of the DF site each characteristic, for example, foF2, is given as foF2(λ, Ψ) = foF2m (1 + C7Δλ + C8ΔΨ) (1 + CλΔλ + CΨΔΨ). The coefficients C7 and C8 for any given azimuth direction are determined with the use of the Union Radio Scientifique Internationale/CCIR coefficients (which are also used in IRI), and the calculation of Cλ and CΨ makes use of the measured ionospheric tilt data; foF2m is the local, measured foF2 value. When the measured density profile and tilt data are available, the derived 3‐D density distribution represents the instantaneous ionosphere structure near the site. The numerical ray tracing includes the effects of the magnetic field and properly treats the spitze effect, making the ray‐tracing program especially useful for small distances. Ray tracing through simulated tilts shows that the differences in ground distances for one‐hop high‐frequency (HF) propagation vary from about 1 to 100 km depending on the assumed tilts and distances. Operational tests for distances up to approximately 100 km have demonstrated good results in determining the transmitter location in real time and have illustrated the importance of using the actual ionospheric profiles and tilts in the ray tracing.

We have investigated the solar activity dependence of the electron density at equatorial and low latitudes using 6 years (a) of measurements between 1 August 2000 and 1 August 2006 from CHAMP and compared it with the international reference ionosphere (IRI) model. The solar activity dependence observed by CHAMP at 400 km altitude exhibits significant variation with latitude, season, and local time. First, the electron density in the crest regions of the equatorial ionization anomaly (EIA) grows roughly linearly from solar minimum to solar maximum, with a higher growth rate than that in the EIA trough region. Second, the solar activity dependence in the EIA crest regions varies strongly with season. The growth rate of the electron density with increasing solar activity around equinoxes is about 1.5 to 2 times greater than that near solstices. Third, the solar activity dependence of the EIA structure varies significantly with local time. In the noon sector the crest‐to‐trough ratio (CTR) obtained at 400 km altitude varies within only a small range between 1.14 and 1.43 from solar minimum to solar maximum. In the postsunset local time sector, however, the CTR grows remarkably with solar activity level, reaching values of above 3.9 at solar maximum. These differences are attributed to the different solar activity dependence of the vertical plasma drift in corresponding local time sectors. The IRI model was found to reproduce the equatorial electron density well near 400 km in the noon sector at all solar activity levels. However, it significantly overestimates it in the postsunset to premidnight sector at high solar activity levels. The major cause for this overestimation has been found to be the IRI's inadequate representation of the F2 layer maximum height (hmF2) in this sector, while the IRI's lack of equatorial spread F seems to play only a minor role.

Very Low Frequency (VLF) remote sensing technique is used to probe the D-layer modeling for which we use a very conventional model known as Wait <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">′</sup> s 2-component ionospheric model. This model is characterized by two ionospheric parameters which are ‘steepness parameter’ (β) and ‘effective reflection height’ (h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">′</sup> ). International Reference Ionosphere (IRI 2012) model is an empirical standard model of the ionosphere, based on all available data sources. In this paper, we compute an electron density profile of the ionospheric D-layer by using IRI model under an ionospheric quiet condition for the year 2016 from altitude range 65 km to 85 Km at the VLF reception station IERCOO/ICSP, Sitapur [Lat 22.5 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">◦</sup> N, Lon 87.48 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">◦</sup> E]. By numerically best fitting, we compare it with Wait <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">′</sup> s empirical formula. Using an auto-generated process we repeat this procedure for several times and computed an authorized data set of Wait <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">′</sup> s parameters (β and h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">′</sup> ) for four locations viz. Kolkata, Kathmandu, Pune, and Bhuj for the different time of the day and for the entire year. Using linear equation as a best fit to the altitude profile, we try to compute the actual data set of β and h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">′</sup> for the entire path of the various location of India and its subcontinent for VTX (18.2 kHz) transmitter for summer (July, 2009) and winter (December, 2008) period. By this data set, we showed the seasonal and diurnal variation of these two characteristic parameters behaviors and also using these parameters and Long Wavelength Propagation Capability (LWPC), we generate a spatio-temporal profile of simulated VLF signal amplitude for several baselines.