Adaptation of the bottomside electron density profile of the IRI model to data of topside radiosounding

Abstract

A method is proposed for reconstructing the electron density profiles N(h) of the IRI model from ionograms of topside satellite sounding of the ionosphere. An ionograms feature is the presence of traces of signal reflection from the Earth's surface. The profile reconstruction is carried out in two stages. At the first stage, the N(h) –profile is calculated from the lower boundary of the ionosphere to the satellite height (total profile) by the method presented in this paper using the ionogram. In this case, the monotonic profile of the topside ionosphere is calculated by the classical method. The profile of the inner ionosphere is represented by analytical functions, the parameters of which are calculated by optimization methods using traces of signal reflection, both from the topside ionosphere and from the Earth. At the second stage, the profile calculated from the ionogram is used to obtain the key parameters: the height of the maximum hmF2 of the F2 layer, the critical frequency foF2, the values of B0 and B1, which determine the profile shape in the F region in the IRI model. The input of key parameters, time of observation, and coordinates of sounding into the IRI model allows obtaining the IRI-profile corrected to real experimental conditions. The results of using the data of the ISIS-2 satellite show that the profiles calculated from the ionograms and the IRI profiles corrected from them are close to each other in the inner ionosphere and can differ significantly in the topside ionosphere. This indicates the possibility of obtaining a profile in the inner ionosphere close to the real distribution, which can significantly expand the information database useful for the IRTAM (IRI Realmax Assimilative Modeling) model. The calculated profiles can be used independently for local ionospheric research.

Introduction

Empirical modeling of the environment state is one of the most important topics of ionospheric research due to a variety of practical applications. Among the large number of models, the most widely used is the IRI model, which is constantly being improved in the form of different versions (Bilitza, 2018). The latest version is the IRI-2016 (Bilitza et al., 2017). The most important issue is assimilation of real-time data into the IRI model. Assimilation of the F2 peak plasma frequency foF2 and the F2 peak height hmF2 was provided for in the first versions. Currently, the decision of this issue has led to the development of a large number of assimilation methods. In the paper (Pignalberi et al., 2018a), focused on the propagation of radio waves in a certain area, a method for assimilating the real-time data into the IRI model, called the International Reference Ionosphere UPdate (IRI UP) method, is described. In this method, the experimental values of the foF2 and the propagation factor M(3000)F2 of several ionosondes are used to construct the maps of the effective indices IG12_eff and R12_eff in a given region by means of the Universal Kriging method (UKM). By using these values as input to the IRI model, its new parameters are close to real-time values. In the paper (Pignalberi et al., 2018b), the IRI UP method was improved by replacing the UKM procedure with a new quality check routine (NQCR). New method was tested using data from 12 European base stations and two test stations during 30 magnetic storms of different intensity between January 1, 2004, and December 31, 2016. Statistics showed a decrease in RMSE for foF2 in MHz and in % approximately 2 times compared to the IRI model. For hmF2 these values in km and % were decreased 1.5 times. However, as noted in (Galkin et al., 2012), the use of effective solar indices gives good results for local areas, but not on a global scale. For this, the paper (Galkin et al., 2012) presented the advanced method of the global ionospheric specification called Real-Time Assimilative Mapping (RTAM), using data from the Global Ionospheric Radio Observatory (GIRO) (Reinisch and Galkin, 2011). In the IRI-RTAM approach, the coefficients of the spherical expansions of the parameters are changed, ensuring proximity of values to the experimental ones. In the paper (Pietrella et al., 2018), the possibility of assimilation of N(h)-profiles was investigated. For this, authors used the ray tracing program in the quasi-vertical propagation mode. The test was carried out on several models in the Mediterranean area, including the IRIEup model, which is a modification of the IRI UP model for the selected European region. The experimental and calculated values of foF2, experimental and calculated ionograms for different models were compared during the period of three magnetic storms. Despite the difference in the methods for processing ionograms, the difference in the number of ionosondes, and the intensity of disturbances, the conclusion turned out to be obvious: assimilation improves the agreement between the experimental and calculated values of foF2 in comparison with the climatological IRI model. It is not clear only why ionograms and N(h)-profiles for the IRI model adapted to the experimental foF2 are not shown. Since the N(h)-profile can also be considered a parameter of the model, there are publications improving the profile shape. It should be noted that the IRI model provides for adaptation to the shape parameter B0. The big attention to this problem is paid in the paper (Themens et al., 2019) within the framework of the new model the Empirical Canadian High Arctic Ionospheric Model (E-CHAIM) (Themens et al., 2017). This model was developed, as an alternative to the IRI model, to improve the determination of ionospheric parameters in the region of geomagnetic latitudes exceeding 50° N. The paper (Themens et al., 2019) proposes a new form of the N(h)-profile of the bottomside and introduces additional new parameters in the scale thickness domain of layers to better describe this form. This allows overcoming discontinuities of the profile in space and time and in the vertical electron density gradient. Such a shape is presented as a single semi-Epstein layer with an altitude-varying scale height (H(h)).

All this corresponds to the growing requirements for accounting and mitigating the effects of space weather in a broad sense, to which the attention has been paid in the roadmap for 2015–2025 presented in (Schrijver et al., 2015). Therefore, the search for new opportunities for assimilation continues. If in previous papers, data from ground-based ionosondes were used, now data from satellites are widely involved. Thus, the model (Shubin, 2015) for hmF2, which is a default option in the IRI-2016 model, was constructed from satellite data. As noted in (Galkin et al., 2012), the IRI-RTAM system is open for real-time data from topside ionospheric sounders. In the paper (Branitskii et al., 2020), it is proposed and realized a principle of the high-speed ionosonde, allowing one to obtain variations of N(h)-profiles with the time resolution 2 s and faster. It is noticed, that this principle can be of great importance for topside sounding. In the paper (Ivanov et al., 2019), the possibilities of using various types of satellite sounding for monitoring the state of the ionosphere are shown. In the present paper, topside radiosounding data are used to correct the profile of the bottomside of the ionosphere in the IRI model.

Many ionograms of topside sounding of the ionosphere (TS), in addition to traces of reflections of sounding signals from the topside ionosphere, also contain traces of signal reflections from the Earth's surface. In fact, the latter are signals of vertical transionospheric sounding (TIS), implemented in a natural way without the use of special equipment. In this paper, we propose a method for using the group paths of these signals to obtain the vertical distributions of the electron density (N(h)-profiles) in the entire thickness of the ionosphere below the satellite height h_s. The main problem is to reconstruct the height distribution of plasma in the bottomside ionosphere.

Authors of papers (Denisenko and Sotsky, 1987, Danilkin et al., 1988) have shown, that the problem of determining the N(h)-profiles in the bottomside ionosphere using the group signal paths penetrating it is reduced to solving the Fredholm integral equation of the first kind. Such problems belong to the class of ill-posed problems in mathematical physics (Tikhonov and Arsenin, 1979) characterized by the lack of solution stability with respect to various kinds of random errors in experimental data. In other words, it is possible to obtain an infinite set of N(h)-profiles, each of which satisfies the available experimental data within the experimental error. Model experiments with the use of the regularization method (Tikhonov and Arsenin, 1979) showed that the reconstruction of the initial N(h)-profile in the bottomside ionosphere, described by three parameters, requires the accuracy of the group signal paths of TIS not less than 1 km (Danilkin et al., 1987). Since the experimental data available today do not possess such an accuracy, to increase the stability of the problem it is necessary to attract additional information about the required solution. The smaller the number of parameters to describe it is, the higher its stability concerning experimental data errors. Therefore, the maximum stability of the problem is provided by model distributions described by the minimum number of parameters. This can be, for example, a parabolic or quasi-Gaussian distribution N(h), which most adequately describes the altitude variation of the electron density in the vicinity of the peak height of the F2 region. However, even in this case, the solutions are not always acceptable from a physical point of view (Danilkin et al., 1987).

The aim of this paper is to develop and test a technique for reconstructing the N(h) -profiles of the bottomside ionosphere in terms of the electron plasma frequency, f_N(h)-profiles, using the ionograms of topside sounding (TS) in the presence of reflections from the Earth's surface. To solve this problem, a correction of the IRI-2016 model (Bilitza et al., 2017) is used below the peak height of the F2-region. The abbreviation IRI will be used to reduce the notation.