International Journal of Navigation and Observation

Volume 2016, Article ID 7016208, 15 pages

http://dx.doi.org/10.1155/2016/7016208

## The Use of the Total Electron Content Measured by Navigation Satellites to Estimate Ionospheric Conditions

Institute for Physics, Southern Federal University, St. Stachki 194, Rostov-on-Don 344090, Russia

Received 20 July 2016; Accepted 6 September 2016

Academic Editor: Sandro M. Radicella

Copyright © 2016 Olga Maltseva and Natalia Mozhaeva. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Measurements of delays of the signals radiated by transmitters of navigational satellites allow us to obtain the total electron content (TEC). In addition, measurements of TEC allow solving problems such as development of local, regional, and global models of TEC and correction of ionospheric delay for increasing accuracy of positioning. Now, it is possible to set the task of calculation of critical frequency foF2 with the use of experimental values of TEC in a global scale. For this purpose it is necessary to know an equivalent slab thickness of the ionosphere which is a coefficient of proportionality between TEC and a maximum density of the ionosphere. The present paper is devoted to the analysis of investigation and utilization of this parameter. It is shown that (1) existing models of *τ* are not empirical and not always can provide an adequate accuracy of foF2 calculation, (2) experimental median (med) provides much larger accuracy of foF2 calculation than the empirical model and variations from day to day and allows filling gaps in the ionosonde data, and (3) it is possible to use a hyperbolic approximation and coefficient for development of a global model of .

#### 1. Introduction

With the advent of navigation satellites, it became possible to measure the total electron content TEC of the ionosphere, which in turn is essential for the functioning of navigation, telecommunications, and other systems. For example, in paper [1], two categories of radio systems were described in terms of ionospheric dependence. The first category includes systems that rely on the critical frequency of the ionosphere foF2: MF and HF communication, HF broadcasting (“short-wave” listening), OTH radar surveillance, HFDF, and HF SIGINT. The operation of these systems requires knowing the behavior of this frequency. Systems of the second category, namely, satellite and navigation (e.g., GPS and GLONASS) communication, space-based radar and imaging, terrestrial radar surveillance, and tracking and others, are influenced by the ionosphere. If in the first case it is necessary to know the state of the ionosphere at the bottom side, namely, up to the maximum height of the layer F2, hmF2, in the second case it is necessary to know the density of electrons in the topside ionosphere (above hmF2) and higher up to the height of high-altitude satellites. A model profile of this part may be corrected by TEC. To solve this problem it is also necessary to know foF2; therefore, one of the most important applications of TEC measurements using navigation satellites is to estimate foF2. Traditionally, values of foF2 are measured by ground-based ionosondes, but their network is sparse. Measurement of TEC has several advantages: a large number of signal receivers, the possibility of continuous, global monitoring, and availability of initial data using network. These advantages allow scientists to study local, regional, and global features of ionospheric behavior independently, quickly, and simultaneously. Definition of morphological and perturbed features has allowed promoting essentially in understanding of spatial and temporary variations of the ionosphere. TEC is widely used for development of local, regional, and global models of TEC, for example, [2–4], which are necessary for correction of ionospheric delays to increase accuracy of positioning [5, 6]. With use of TEC ionospheric disturbance indexes were developed [7, 8]. In the present paper the basic attention is given to problem of estimation of foF2 using TEC measurements. To calculate foF2 using TEC it is necessary to know a proportionality coefficient between TEC and NmF2. This coefficient is an equivalent slab thickness *τ* of the ionosphere. This paper is devoted to joint use of the observational values of TEC(obs) and the equivalent slab thickness *τ* to estimate foF2. The opportunity of development of a global *τ* model is investigated.

#### 2. Methodology and Used Data

To obtain ionospheric conditions, in particular, values of foF2, empirical models are widely used, for example, IRI and NeQuick. These models define an average condition of the ionosphere; however for functioning of modern systems it is necessary to know instantaneous values and variations of foF2 from day to day. In the present paper, the instantaneous values of TEC measured by means of navigating satellites are used to estimate these values and variations. The methodology of foF2 estimation, used in this paper, consists of joint use of observational values TEC(obs) and an equivalent slab thickness *τ* of the ionosphere. The following options are considered: (1) *τ*(IRI) of the IRI model [9], (2) of the Neustrelitz models, (3) the model of Muslim and coauthors [10], and (4) median (med) of observational values *τ*(obs). *τ*(IRI) is traditionally used [11–13]. Besides, the IRI model is the international standard to which results of other models are usually compared. The model = TEC(NGM)/NmF2(NGM) is actually used in [14] on the basis of Neustrelitz models for TEC and NmF2 [15, 16], but without sufficient validation. This model has been tested in [17]. It was obtained that use of *τ*(NGM) did not improve results of use of *τ*(IRI) in most cases. Authors of [18] complained that researchers develop ionospheric models but not a model of *τ*. Meanwhile, authors of [17] only have shown the values for the 6 stations in different regions of the globe. Moreover, values of *τ*(obs) were calculated from ionospheric electron content IEC values, that is, in the range of heights from the bottom of the ionosphere to the height of 500 km while TEC is measured for the satellite altitude (about 20,000 km). The latest step has been done in [10], where a model of average values of *τ* was developed by expansion in Fourier series according to the TEC of 21 stations. For TEC, monthly averages of the global CODE map were taken, and for foF2, the monthly medians. To test the model, data of 13 stations were used in such a way as to get results for various latitude zones (low, mid, and equatorial). The results were obtained for quiet and disturbed conditions by comparison with the results of the IRI model that takes into account STORM factor. The assumptions made in developing the model are as follows: (1) a linear dependence of all parameters (TEC, foF2, *τ*) on solar activity, (2) absence of longitudinal dependence of these parameters at the same local time LT, (3) transition from a geographic to a geomagnetic coordinates does not affect the dependence of parameter variations on LT, and (4) invariance of *τ* in quiet and disturbed conditions. Results were obtained for 5 magnetic storms of varying intensity in the period 2000–2014. They are described in detail for several stations and individual disturbances. The general conclusions are as follows: (1) the new model enables improved compliance with measurements compared with the model IRI-STORM in the mid- and low latitudes and (2) the model gives the deterioration in equatorial latitudes in quiet and disturbed conditions. However, as could be seen from Table of paper [10], deterioration takes place in quiet conditions even for the midlatitude Chilton station and for the low-latitude Del’Ebre station. Probably, it is connected with that the assumptions, taken as a principle of model, are not absolutely strict. In particular, it is possible to show that *τ*(med) depends on solar activity in the nonlinear way. The authors themselves point out that the presence of longitudinal dependence can be the cause of the deterioration. Illustration of violation of the assumption (2) is given in Figure 1 for stations in different zones for March 2015. Figures are given for *τ*(med) and *τ*(IRI) in (a) midlatitude zone, (b) low latitudes, and (c) an equatorial region. Latitudes of couples of stations are very close. Couple Juliusruh-Novosibirsk belongs to midlatitudes and couple Nicosia-Kokubunji is located in low latitudes. Couple Sao Luis-Fortaleza is in the equatorial zone. Authors of [10] do not apply their model to high latitudes and auroral zones; however, as in the papers [19, 20] the possibility of using the IRI model in these areas was shown; results are given also for couple Tromsö-Amderma. The parameter, for which the plot is under construction, is moved in heading together with units of measurements. On an axis , local time LT is postponed.