The Scientific World Journal

Volume 2015, Article ID 376702, 11 pages

http://dx.doi.org/10.1155/2015/376702

## Ionospheric Correction Based on Ingestion of Global Ionospheric Maps into the NeQuick 2 Model

^{1}School of Electronic Information, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, China^{2}China Research Institute of Radiowave Propagation, No. 36 Xianshandong Road, Qingdao 266107, China^{3}University of Chinese Academy of Sciences, Beijing 100029, China^{4}Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China^{5}The Abdus Salam International Center for Theoretical Physics, T-ICT4D Laboratory, 34100 Trieste, Italy^{6}The Constellation Observing System for Meteorology, Ionosphere, and Climate Program Office, University Corporation for Atmospheric Research, Boulder, CO 80303, USA

Received 18 June 2014; Revised 18 August 2014; Accepted 19 August 2014

Academic Editor: Zhaojin Rong

Copyright © 2015 Xiao Yu et al. 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

The global ionospheric maps (GIMs), generated by Jet Propulsion Laboratory (JPL) and Center for Orbit Determination in Europe (CODE) during a period over 13 years, have been adopted as the primary source of data to provide global ionospheric correction for possible single frequency positioning applications. The investigation aims to assess the performance of new NeQuick model, NeQuick 2, in predicting global total electron content (TEC) through ingesting the GIMs data from the previous day(s). The results show good performance of the GIMs-driven-NeQuick model with average 86% of vertical TEC error less than 10 TECU, when the global daily effective ionization indices (Az) versus modified dip latitude (MODIP) are constructed as a second order polynomial. The performance of GIMs-driven-NeQuick model presents variability with solar activity and behaves better during low solar activity years. The accuracy of TEC prediction can be improved further through performing a four-coefficient function expression of Az versus MODIP. As more measurements from earlier days are involved in the Az optimization procedure, the accuracy may decrease. The results also reveal that more efforts are needed to improve the NeQuick 2 model capabilities to represent the ionosphere in the equatorial and high-latitude regions.

#### 1. Introduction

The ionosphere, the ionized part of the atmosphere extending from ~60 to several thousand kilometers above the Earth surface, can affect the radiowave signals travelling through it in different ways, such as Faraday rotation, doppler frequency shift, ray path bending, carrier phase advance and pseudorange group delay, and fluctuations of signal intensity and phase (ionospheric scintillation) [1–4]. Regarding the L band of the Global Navigation Satellite System (GNSS) signal, the major influence of the ionosphere is the carrier phase advance and pseudorange group delay on ranging signals depending on the ionospheric total electron content (TEC, Unit: TECU, 1 TECU = 10^{16} el/m^{2}). For code measurements, the consequent pseudorange delay due to the ionosphere Ig[m] can be described as a first approximation by

Here, the slant TEC (sTEC) is defined as the integral of the electron density along the path from the transmitter to the receiver. As it is well known, the GNSS single frequency receivers have to compensate for the unwanted term Ig, before solving the navigation equations. In this case an explicit estimate of the TEC is usually obtained by means of an ionospheric model.

Several models that could be used to calibrate the ionospheric term have been developed and are still hot topics of investigation for navigation-related applications. The GPS ionospheric correction algorithm (ICA), known as Klobuchar model [5], designed on the basis of the Bent model, introduces many geometric approximations aiming at reducing the receiver computational load. The Klobuchar model provides a daily vertical TEC (vTEC) profile consisting of a cosine representation during the day and a constant value during the night. Both the amplitude and period of the cosine term are represented by four broadcast coefficients defining a third order polynomial of the geomagnetic latitude. The phase of the maximum is fixed at 14:00 local time. Through a thin shell ionosphere assumption, a suitable mapping function is applied to convert the vertical time delay at the pierce point to a slant delay along a given ray path. The GPS ICA is supposed to provide a 50% correction of the ionospheric time delay and the interested reader is referred to [5] for a detailed description of the algorithm.

The Galileo ICA can be described as follows. The effective ionization parameter (Az) at each monitoring station is determined through minimizing the differences between observed and NeQuick modeled slant TEC values for the given day (it is assumed that Az will be valid for the following day). From the calculated Az at different monitoring stations, a global Az is determined as a function of Modip using a 2nd degree polynomial determining a set of 3 coefficients. Then the satellite transmits the relevant Az in the navigation message in terms of 3 coefficients. The receiver calculates slant TEC using NeQuick with the broadcast ionization parameters and corrects the ionospheric delay at the specific frequency [6–10].

Some excellent work about the performance of the Galileo-like model in providing the ionospheric delay predictions has been published [7–10]. In these assessment studies, some IGS stations were used as reference stations to create the broadcast message and the others were used as test stations to obtain the slant TEC mismodeling. In [7], the performance in the equatorial region and northern mid-latitude region during May 2000 is given by the probability density function of residual error. In [8], a comparison of the results obtained by the GPS and Galileo operational models with observations is presented in terms of the year 2000 daily 65 percentile and 95 percentile of the absolute values of the mismodelings. In [9], the performance of the NeQuick model in correcting the ionospheric delay was obtained by comparing its predictions with Topex/Poseidon TEC data of 3 March 2000. In [10], slant TEC data for the year 2002 were ingested into NeQuick for a dozen locations around the world where colocated ionosonde and GPS receiver allow comparing measured and modeled TEC values. The dataset used by these studies covers a single day, a whole month or year during high solar activity, and their results indicate that the performance of Galileo ICA is better than GPS ICA and can be used to correct the observed ionospheric delay in a realistic way.

In the present work, a long history (over 13 years) of global ionospheric maps (GIMs) is adopted as the primary source of data to investigate the capabilities of NeQuick 2 model in providing global daily TEC prediction in a statistical way. Section 2 gives a short description of NeQuick 2 model and dataset. Section 3 describes the ionospheric correction algorithm based on NeQuick 2 adaption to GIMs in a Galileo-like mode and the criteria used to carry out the assessment. Section 4 presents and discusses the results and also a test study to improve the model performance further. Conclusions are then drawn in Section 5.

#### 2. NeQuick 2 Model and Dataset

NeQuick 2 [11] is the latest version of a quick-run ionospheric electron density model particularly tailored for transionospheric propagation applications, developed at the Aeronomy and Radio Propagation Laboratory (ARPL, now T/ICT4D) of The Abdus Salam International Center for Theoretical Physics (ICTP), Trieste, Italy, and at the Institute for Geophysics, Astrophysics and Meteorology (IGAM) of the University of Graz, Austria.

To describe the electron density of the ionosphere, the NeQuick model uses a DGR profile formulation, which is proposed by di Giovanni and Radicella [12] and subsequently modified by Radicella and Zhang [13] and Radicella and Leitinger [14]. The model describes the ionosphere separately for the bottomside and the topside. The bottomside goes from 60 km to the F2-layer peak and consists of a sum of five semi-Epstein layers. The topside is above the F2 peak layer and it is described by means of a semi-Epstein layer with a height-dependent thickness parameter. To compute the thickness parameters and the peak electron density and height for the Epstein layers, NeQuick employs the ionosonde parameters which can be modeled or experimentally derived. The major changes in the representation of the topside and bottomside in NeQuick 2 can be found from [15, 16].

NeQuick 2 outputs the ionospheric electron density and TEC as well for the given location, time of the day, season, and solar activity indices. In order to improve the model performance and prediction capabilities, data ingestion and assimilation techniques have been implemented [6–10, 17–20], which replace the standard solar activity indices with different “effective” parameters that allow adapting a model to a specific data set. These techniques become part of COST296 Action course [21–23].

In this study, GIMs are chosen as measured values for convenience [24–27]. GIMs are computed based on the International GNSS Service (IGS) network where GPS receivers are distributed worldwide. There are at least five analysis centers that generate and deliver long-term GIMs: CODE, EMR, ESA, JPL, and UPC. Different agencies may use different reference frames and techniques to estimate vTEC and differential code biases (DCB). After computation, three validation centers (JPL, ESA, and UPC) combine them into a common IGS GIM. The global accuracy of this combined TEC is about 2–8 TECU depending on the epoch in the solar cycle, season, latitude, and proximity of available GPS receivers [28].

We choose GIMs computed by JPL (Jet Propulsion Laboratory) and CODE (Center for Orbit Determination in Europe) as measured values. GIMs generated at both agencies use data from more than 100 GPS sites of the IGS and other institutions. At JPL, the vertical TEC is modeled in a solar-geomagnetic reference frame using bicubic splines on a spherical grid, and a Kalman filter is used to solve simultaneously instrumental biases and vTEC on the grid (as stochastic parameters). More details about the JPL GIM algorithm and daily process can be found in [29–31]. At CODE, the vertical TEC is modeled in a solar-geomagnetic reference frame using a spherical harmonics expansion, and piecewise linear functions are used for the representation in the time domain. Daily DCB for all GPS satellites and ground stations are estimated simultaneously as constant values for each day. More details about the CODE GIM algorithm and daily process can be found in [32–34].

At both agencies, the GIMs are computed every 2 hours. From its beginning to 3 November 2002, the GIMs represented global TEC distribution at odd-hours and then they switched to even-hours. The vertical TEC values in the grids are given along the geographic latitude and longitude, from 87.5°S to 87.5°N and 180°W to 180°E, with intervals of 2.5° and 5°, respectively. The period of data used in this paper spans from its beginning to 31 December 2011. The CODE GIMs start from 28 March 1998 and the dataset is perfectly complete and spans 5027 days. The JPL GIMs start from 28 August 1998 and are not available on several days and they span 4856 days.

As an example, Figure 1 presents 12 JPL GIMs on 15 March 2006 (10.7 = 73.4, low solar activity), where the features of equatorial anomaly are quite evident. In each panel, the -axis and -axis represent geographic longitude and latitude, respectively, and the color scale indicates the TEC in TECU.