PUBLICATIONS. Journal of Geophysical Research: Space Physics. Spherical cap harmonic analysis of the Arctic ionospheric TEC for one solar cycle

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1 PUBLICATIONS RESEARCH ARTICLE Special Section: The Causes and Consequences of the Extended Solar Minimum between Solar Cycles 23 and 24 Key Points: SCHA has adequate accuracy for the mapping and prediction of the Arctic TEC SCHA is able to track TEC distribution, variation, and ionization patches GNSS and SCHA provide a promising approach for analyzing the Arctic TEC Correspondence to: J. Liu, jingbin.liu@fgi.fi Citation: Liu, J., R. Chen, J. An, Z. Wang, and J. Hyyppa (2014), Spherical cap harmonic analysis of the Arctic ionospheric TEC for one solar cycle, J. Geophys. Res. Space Physics, 119, , doi: / 2013JA Received 30 SEP 2013 Accepted 19 DEC 2013 Accepted article online 28 DEC 2013 Published online 30 JAN 2014 Spherical cap harmonic analysis of the Arctic ionospheric TEC for one solar cycle Jingbin Liu 1, Ruizhi Chen 2, Jiachun An 3, Zemin Wang 3, and Juha Hyyppa 1 1 Department of Remote Sensing and Photogrammetry, Finnish Geodetic Institute, Masala, Finland, 2 Conrad Blucher Institute for Surveying and Science, Texas A&M University Corpus Christi, Corpus Christi, Texas, USA, 3 Chinese Antarctic Center of Surveying and Mapping, Wuhan University, Wuhan, China Abstract Precise knowledge of the Arctic ionosphere total electron content (TEC) and its variations has scientific relevance due to the unique characteristics of the polar ionosphere. Understanding the Arctic TEC is also important for precise positioning and navigation in the Arctic. This study utilized the spherical cap harmonic analysis (SCHA) method to map the Arctic TEC for the most recent solar cycle from 2000 to 2013 and analyzed the distributions and variations of the Arctic TEC at different temporal and spatial scales. Even with different ionosphere conditions during the solar cycle, the results showed that the existing International Global Navigation Satellite Systems Service stations are sufficient for mapping the Arctic TEC. The SCHA method provides adequate accuracy and resolution to analyze the spatiotemporal distributions and variations of the Arctic TEC under different ionosphere conditions and to track ionization patches in this polar region (e.g., the ionization event of 26 September 2011). The results derived from the SCHA model were compared to direct observations using the Super Dual Auroral Radar Network radar. The SCHA method is able to predict the TEC in the long and short terms. This paper presented a long-term prediction with a relative uncertainty of 75% for a latency of one solar cycle and a short-term prediction with errors of ±2.2 total electron content units (TECUs, 1 TECU = el m 2 ), ±3.8 TECU, and ±4.8 TECU for a latency of 1, 2, and 3 days, respectively. The SCHA is an effective method for mapping, predicting, and analyzing the Arctic TEC. 1. Introduction Human activities such as resource utilization, scientific research, air and marine traffic, and resource exploration are currently increasing in the Arctic region. The sovereignty of the Arctic is a politically important topic because natural resources are becoming exhausted, and new resources are being sought in the Arctic regions. In addition, with receding polar ice, the Northwest and Northeast Passages are now considered as possible new routes that will increase transportation efficiency. Oil exploration is also increasing in Arctic regions. Finally, search and rescue operations are likely to increase due to increasing transportation through the area. Thus, reliable Global Navigation Satellite Systems (GNSS) positioning and navigation solutions in the Arctic are becoming ever more important. Ionospheric disturbances can be severe at high latitudes due to the proximity to the polar cap, which is connected to the solar wind via open magnetic field lines. Thus, the Arctic is a highly variable environment, both spatially and temporally. Ionospheric models used for satellite-based augmentation systems (SBASs) often suffer from a large grid size and an insufficient number of measurements. The ionospheric plasma exhibits dispersive effects on radio signals that lead to several difficulties, including phase advance, code delay, phase and amplitude scintillation, and a loss of lock for GNSS signals [Jakowski et al., 2005]. These effects are directly connected to the total electron content (TEC) and gradients of the TEC within the ionosphere. In addition, the Arctic regions are located within or close to the polar cap, which is connected to the highly variable solar wind by open magnetic field lines. This effect, in connection with changes in solar illumination, leads to changes over temporal (e.g., diurnal, seasonal, and solar cycles) and spatial scales (small, medium, and large scales). In Arctic regions, these ionospheric effects are particularly important due to the low elevation of the GPS (Global Positioning System) and Galileo orbits, resulting in a longer signal path through the ionosphere. Aquino et al. [2009] discovered that the scintillation index S4 increases for the GNSS satellites at low elevations observed at high latitudes. LIU ET AL American Geophysical Union. All Rights Reserved. 601

2 Unlike the equatorial region, where the ionosphere is affected more directly by solar activity, the ionosphere of the Arctic region is also driven by electron precipitation and irregularities in electron density [Skone, 1998]. Therefore, the ionospheric activity of the Arctic region differs substantially from that of the equatorial region; for example, electron precipitation leads to the auroral light at night. As a consequence, in the Arctic region, the ionosphere exhibits much greater irregularity compared to other regions, and the total electron content of the ionosphere is even more difficult to model for the following two reasons: 1. The ionospheric TEC variation in the Arctic is much more complicated than in other regions, and commonly used models, such as the Klobuchar model, Global Ionosphere Model (GIM), and International Reference Ionosphere (IRI) model, are estimated using data that are observed at low and middle latitudes rather than Arctic latitudes [He et al., 2011]. 2. The conventional ionosphere models based on geodetic coordinates have different spatial resolutions in the east-west and north-south directions, especially in the area close to the pole. The IRI model is the internationally recognized and recommended standard for the specification of plasma parameters in Earth s ionosphere [Bilitza et al., 2011]. This model describes monthly averages of the electron density, electron temperature, ion temperature, ion composition, and several additional parameters in the altitude range from 60 to 1500 km. IRI is a data-based empirical model based on most of the available and reliable sources of ionospheric plasma data. These data sources include the worldwide network of ionosondes that has monitored ionospheric electron densities at and below the F peak for more than half a century and the powerful incoherent scatter radars that measure plasma densities, temperatures, and velocities throughout the entire ionosphere; unfortunately, the latter data are available only at a few selected locations (approximately eight in operation as of 2011) [Bilitza et al., 2011]. Due to the complicated structure of the polar ionosphere, the nonuniform distribution of ionosonde stations, and the paucity of data from polar sectors (both north and south), the inclusion of high-latitude characteristics in IRI modeling remains an ongoing, high-priority topic for IRI researchers [Szuszczewicz et al., 1993; Bilitza, 1995; Zhang and Paxton, 2008]. Ionospheric parameters deduced from GNSS measurements represent a promising new resource for improving the IRI model and are an excellent candidate for data assimilation into the IRI model [Hernández- Pajares et al., 2009; Bilitza et al., 2011]. Of greatest interest are electron density profiles deduced via tomography and occultation, and integral measurements (TEC) are widely used for space weather applications [Garner et al., 2008]. The ongoing validation of these techniques has been successful [Bilitza et al., 2011]. Komjathy et al. [1998] were among the first to assimilate global TEC maps deduced from GPS measurements into the IRI model to update the monthly average model based on the daily and hourly ionospheric conditions monitored by GPS. Hernandez-Pajares et al. [2002] directly used individual slant TEC measurements to adjust IRI model parameters. More recently, Schmidt et al. [2008] and Zeilhofer et al. [2009] developed a 4-D representation of the ionospheric electron density. Other IRI-GPS assimilation schemes have been developed, such as the work of Fuller-Rowell et al. [2006], who used IRI-deduced empirical orthogonal functions to represent the TEC over the continental U.S. (US-TEC), and Angling et al. [2009], who used IRI and GPS data in their electron density assimilative model. To map and predict the regional TEC with comparable accuracy, Liu et al. [2008a, 2011] presented a regional model based on the spherical cap harmonic analysis (SCHA) method. This approach is used to model the TEC values distributed over a spherical cap using the spherical cap harmonic functions [Haines, 1988]. Unlike the conventional approaches in which the future TEC is predicted by extrapolation from an existing model, the spherical cap harmonic analysis approach utilizes models of the past to predict the future models; the future TEC is then predicted via the predicted models. This method has been applied to modeling the ionospheric TEC observed by the Australian Regional GPS Network (ARGN), and the obtained results confirm the usefulness of SCHA for near-real-time regional TEC mapping as well as the potential for its application to the modeling of other ionospheric parameters [Zahra et al., 2010]. Liu et al. [2010] presented promising results obtained by mapping the Arctic TEC using the existing International GNSS Services (IGSs) data and products. Natural Resources Canada subsequently used this method to develop the GPS TEC mapping service over Canada [Ghoddousi-Fard et al., 2011]. The present study presents the mapping and prediction of ionospheric TECs of the Arctic region using GNSS data and products and analyzes the distribution and variations of the Arctic ionosphere for the solar cycles LIU ET AL American Geophysical Union. All Rights Reserved. 602

3 from 2000 to The TEC observables derived from the GNSS data were mapped using the spherical cap harmonic analysis model. The ionospheric TEC variations were then analyzed using different spatiotemporal scales in the time and frequency domains. Because ionosphere refraction is one of major error sources in GNSS positioning, the knowledge of ionosphere variations will enable the development of precise positioning services in the Arctic region. As a detailed study case, a geomagnetic storm that occurred on 26 September 2011 was analyzed using the spherical cap harmonic model to map the ionospheric TEC over the Arctic region for this particular day, and various ionization patches were identified via SCHA-derived TEC mapping. The result was then compared to the findings of a paper published in Science [Zhang et al., 2013] that presented the directly observed results of the evolution of the ionization patches, including the formation, polar cap entry, transpolar evolution, polar cap exit, and sunward return flow using the Super Dual Auroral Radar Network (SuperDARN). 2. Regional TEC Mapping Using GPS Data This section outlines the traditional regional TEC models and the SCHA model. The results of these models are compared in the following sections. This section also introduces the data processing methods used for all of the models in this study Deriving TEC From GPS Measurements As the ionosphere is a dispersive medium for radio signals, ionospheric delays of radio signals are a function of the radio frequencies and ionospheric TEC. The slant TEC corresponds to the total number of electrons along a satellite-receiver path and is estimated for each satellite/receiver pair using the geometry-free linear combination of the measurements of a dual-frequency GPS receiver as follows [Bergeot et al., 2010]: TEC k ¼ νðp 2 P 1 Þþν ðb r þ B s Þ (1) where ν ¼ f 2 1 f 2 2 = 40:28 f 2 1 f 2 2 ¼ 9:52437 by taking the frequencies of GPS carriers L1 = GHz and L2 = GHz. TEC k is the TEC observation derived from pseudorange measurements at epoch k, and it has the unit of TECU (1 TECU = electrons m 2 ). P i ði ¼ 1; 2Þ are pseudorange of the corresponding frequency. B r and B s are the receiver and satellite interfrequency hardware delays, respectively, that are included in the IGS ionosphere products. In the work of ionospheric TEC mapping, an idealized single-layer model assumes that all free electrons are contained in a shell of infinitesimal thickness. The idealized layer typically has an altitude (H) of between 350 and 450 km. A mapping function is then used to convert the derived slant TEC to a vertical TEC. In this study, the height of the assumed single layer was selected as H = km, which is close to the optimal approximation of the Chapman profile mapping function that has less than 1% of TEC mapping error [Schaer, 1999]. The mapping function is the triangular function [Sardon et al., 1994]. As shown in equation (1), the noise of GPS pseudoranges has an amplified effect on the accuracy of the TEC estimate. In this study, the method of carrier phase smoothing was used to improve the accuracy of the TEC estimate. When cycle slips are not present or can be recovered and the interfrequency hardware delay biases B are considered stable over a period of a few days [Schaer, 1999], the accuracy of ionospheric TEC estimate can be improved using a recursive smoothing process over time as follows: TeEC k ¼ K 1 K ν ðλ 2 φ 2 λ 1 φ 1 Þ 1 K K K 1 k¼1 ðν ðp 2 P 1 ÞÞ 1 K ðν ðλ 2 φ 2 λ 1 φ 1 ÞÞþν ðb r þ B s Þ k¼1 where TeEC k is the smoothed TEC measurement, P i ; and ϕ i ði ¼ 1; 2Þ are pseudorange and carrier phase measurements of two frequencies, respectively, and K is the smoothing length. We assume that the pseudorange and carrier phase measurements are uncorrelated; thus, the variance of the smoothed TEC can be estimated as follows: σ 2 ¼ K 1 σ Te 2 TEC ECK K ϕ þ 1 K σ2 TEC p þ σ 2 B (3) where σ 2 TEC p and σ 2 TEC ϕ are the variance of TEC measurements derived from the pseudorange and carrier phase measurements, respectively, and σ 2 B is the variance of the hardware delay biases. (2) LIU ET AL American Geophysical Union. All Rights Reserved. 603

4 The variance of the smoothed TEC is used to determine the weight of smoothed TEC measurements in the least squares solution. In this study, the variances of the pseudorange and carrier phase TEC measurements are given as σ TECp ¼ 3 TECU and σ TECϕ ¼ 0:1 TECU, which corresponds to an accuracy of 0.3 m for P code pseudorange measurements and 0.05 cycles for carrier phase measurements. To avoid the overweighting of smoothed TEC measurements, a limit of K 112 is applied to the smoothing process. Consequently, the noise level of the smoothed TEC is σ T e ECK 0:3 TECU Traditional Regional TEC Models For single-frequency receivers, one alternative for mitigating the effect of ionosphere delay is to calculate the TEC value via a TEC model. Some models have a global coverage, while others can cover a specific region as these models are derived from GPS data collected in the corresponding region. Global models such as the Klobuchar model and the GIM have limited coverage and degraded accuracy in the Arctic region. Regional TEC models usually have better mapping accuracy because of the greater station density in the regional GPS networks. Regional TEC models mainly have two categories: one is grid-based models such as the SBAS model, while the other is mathematical function based, e.g., the polynomial model [Schaer, 1999; Liu et al., 2008b; Komjathy, 1997], the triangle series model [Georgiadou, 1994; Georgiadou and Kleusberg, 1988], and the low-degree spherical function model [Wilson et al., 1995]. These three types of basic function models have many variants. The characteristics of these three models are investigated and compared by Liu et al. [2008b] with observations from China. In this study, these models are processed with observation in the Arctic, and their mapping performances in the Arctic region are compared with that of the spherical cap harmonic analysis model. The mathematical functions of these three models can be found in Liu et al. [2010, 2011], and the following parameter configurations were used for the Arctic region in the present study. For the polynomial model, the latitude and longitude of central point of the region are 75 and 0, respectively, with the degree of 7 and the order of 8. Thus, there are 56 model parameters to be estimated. The triangular series model takes the value of TEC as a series function of different effect factors on the ionosphere, such as local time and latitude. The number of model parameters is 15. The low-degree spherical function model has a similar function forma as the global spherical harmonic model [Schaer, 1999; Wilson et al., 1995]. In this study, the degree is 4, and there are 25 model parameters to be estimated. Different with the case of the whole globe, the spherical functions are not the solution of the Laplace s equation over a partial region of the globe, and they are not hence the harmonic functions The Spherical Cap Harmonic Analysis Model The spherical cap harmonic analysis model consists of a set of spherical cap harmonic functions derived by solving a Laplace s equation on a specific spherical cap. A spherical cap has a colatitude range of ([0,θ 0 ]), θ 0 π. When θ 0 = π, the spherical cap harmonic function becomes the traditional spherical harmonic function [Schaer, 1999]. The spherical cap harmonic analysis model of regional TEC is expressed as follows: E v ðθ c ;;λ c Þ ¼ K max minðk;mþ h i ep m n k¼0 m¼0 k ðmþðcosθ c Þ ec m k cos ð mλ cþþes m k sin ð mλ cþ (4) where (θ c,λ c ) is the spherical cap coordinate of the ionosphere pierce point (IPP);E v (β c,λ c ) is the vertical TEC at the IPP (θ c,λ c );K MAX and M are the maximum degree and order of the series, respectively;ep ðcosθþ is the normalized associated Legendre function;and ec m k and es m k are normalized spherical cap harmonic coefficients. In the case of the spherical cap (θ 0 π), the boundary conditions of Laplace s equations are met by real degrees n k (m) rather than integer degrees as in the case of the globe. The real degrees n k (m) are solved by an iterative bisection solution, and k is the index of the real degrees (0 k K MAX ). Additional mathematical representations of the spherical cap harmonic function and the real degrees solution can be found in Haines [1985, 1988], Li [1993], and Liu et al. [2008a]. In the present study, the geographical North Pole is the spherical cap pole of the interested area, and the half angle is 30 (θ 0 =30 ), the maximum degree is 8 (K MAX = 8), and the maximum order is 6 (M = 6). The number of model parameters is 75 in total. 3. Mapping the Arctic TEC Using GPS Data This study compares the three traditional TEC models and the SCHA model for mapping the Arctic TEC using the same GPS measurements and relevant products. These measurements and products include (1) GPS LIU ET AL American Geophysical Union. All Rights Reserved. 604

5 Figure 1. The geographical locations of the IGS tracking stations in the Arctic area. Land is indicated by brown, and sea/ocean is represented by blue. The yellow points indicate the locations of the 44 IGS stations used for estimating the SCHA models, while the magenta points show the seven IGS stations used for verifying the estimated models. measurements from IGS tracking stations, (2) IGS precise orbit data in sp3 format, and (3) Global Ionosphere Mapping products and differential code bias (DCB) products of receivers and satellites provided by the Center for Orbit Determination in Europe (CODE). The IGS tracking stations located above the 55 latitude were used in this study, and their geographical locations are shown in Figure 1. Among these stations, 44 IGS stations, marked as Mapping stations in Figure 1, were used for TEC mapping, and other seven stations, marked as Verification stations, were used for verifying the estimated SCHA models of TEC mapping. The observations of these stations are independent because they use different receivers, although some of stations have close locations. The measurement data set was provided in receiver-independent exchange format by IGS central bureau via ftp access. The sample rate of the GPS measurements is 30 s, and the elevation cutoff threshold is 20 in the data processing. Because the ionospheric TEC is typically related to the local time, this study divides 24 h of one calendar day into 12 sessions with a session length of 2 h. TEC measurements in each session are represented by a set of model parameters. Therefore, there are 12 sets of model parameters for each calendar day. The sp3 satellite orbit products are used to calculate the precise positions of satellites and further calculate the positions of the ionosphere pierce points and elevations of GPS signal paths. The Spline interpolation method is used to interpolate the satellite positions at the observation epochs. The values of the interfrequency hardware biases in equation (1) are retrieved from the DCB products provided by CODE and are removed from TEC measurements. In addition, the GIM products are used as a reference for comparison. The GIM products can be interpolated for calculating the TEC of anytime at any location using the interpolation method presented in Schaer et al. [1998]. 4. Mapping Performance of the Four Models in Temporal and Spatial Scales As noted by Liu et al. [2008a, 2010], these traditional models were originally proposed for lower and middle latitude regions, and they have an optimal performance for specific conditions. For example, the polynomial model is suitable for a small area, and it has been adopted in Bernese GPS analysis software [Dach et al., 2007]. The function expressions of these models are based on two dimensional geographic coordinates (latitude LIU ET AL American Geophysical Union. All Rights Reserved. 605

6 Figure 2. Annually ionospheric TEC mapping performance of the four models at the Arctic region during the most recent solar cycle ( ). and longitude), and they do not consider the noncoherence of spatial scale in the east-west and north-south directions, which becomes particularly large in the Arctic. This study presents comparatively the mapping performance of these models as well as the spherical cap harmonic analysis model for the Arctic region. Figure 2 shows the annual mapping root-mean-square (RMS) errors (top) and the relative errors (bottom) of the four models in the Arctic region during the solar cycles from 2000 to The mapping error is defined as the difference between the model estimate and the TEC measurement, while the relative error is defined as the ratio in percentage between RMS error and mean TEC for a time period. Figure 3 shows the estimated Figure 3. Estimated (top) daily average ionospheric TEC, (middle) solar activity indices, and (bottom) geomagnetic A index during the most recent solar cycle (2000 to 2013). LIU ET AL American Geophysical Union. All Rights Reserved. 606

7 daily average ionospheric TEC; solar activity indices, including the number of sunspots and radio flux; and geomagnetic A index during the period from 2000 to Figures 2 and 3 show that the polynomial model has the worst mapping accuracy, and the triangle series model has significantly larger mapping errors than the spherical function model and spherical cap harmonic analysis model, which have comparable performance. When the ionosphere undergoes active conditions, which are indicated by solar and geomagnetic indices in Figure 3, all of these models have degraded mapping accuracy than that for the calm ionosphere conditions. During the whole solar cycle, the spherical cap harmonic analysis model has mapping RMS errors of less than 5 TECU at most of times, and the mapping error is less than 2 TECU under calm ionosphere conditions during 2006 to The spatial distribution of the mapping residuals is another important measure of mapping performance. Figures 4 and 5 show the spatial distribution of mapping residuals of the spherical cap harmonic analysis model under the most active (December 2002) and calm (December 2008) ionosphere conditions, respectively. These 2 days are close to the southern (winter) solstice of year 2002 and 2008 in the Arctic area, and they have the maximum and minimum ionospheric activity levels separately. Note that Figures 4 and 5 use different color scales. At calm ionosphere conditions, the spherical cap harmonic analysis model has mapping errors of less than 3 TECU for the entire area. At active ionosphere conditions, mapping errors are less than 5 TECU for most of the areas, and they are less than 10 TECU for the whole area. For all ionosphere conditions, the larger errors typically occur at 12 to 14 h local time, which is marked by the magenta lines. During the period of 12 to 14 h local time, the ionosphere TEC typically has the largest amplitude and variation during 1 day [Schaer, 1999; Liu and Gao, 2004]. Lower latitude areas have larger mapping errors because there is more solar radiation than in higher latitude areas in December. The mapping errors of the SCHA model show no boundary effect, which is significant for polynomial models [Liu et al., 2011]. 5. Arctic TEC Spatial Distributions and the Variations With Respect to Local Time The previous section has showed that the spherical cap harmonic analysis model has an adequate mapping accuracy for the entire Arctic region under different ionosphere conditions. From this section, the Arctic ionosphere TEC values estimated by the SCHA model are analyzed in the temporal and frequency domains. Figures 6 and 7 show the ionosphere TEC mapping distribution of spherical cap harmonic analysis modeled for the Arctic region in 1 day under the most active (December 2002) and calm (December 2008) ionosphere conditions, respectively. These days have the maximum and minimum ionospheric activity levels separately. Under active ionosphere conditions (Figure 6), the overall ionosphere TEC level is generally 6 times higher than that during calm ionosphere conditions (Figure 7). For all ionosphere conditions, the ionospheric TEC spatial distribution over the entire arctic region is strongly correlated with the solar radiation, which is related to the local time and latitude. In December, more northern latitude areas receive less solar radiation. This is known as the polar night phenomenon. The series in Figures 6 and 7 show clearly the diurnal variation of the ionosphere TEC over the entire study region. At a given time, ionosphere TEC becomes higher when the local time (longitude) approaches 12 to 14 h and the latitude becomes lower. At a specific location, the ionosphere TEC becomes higher when the local time is closer to 12 to 14 h. In the north polar area, where the polar night occurs in December, the ionosphere TEC remains relatively low throughout the entire day. The spatial distribution of the ionosphere TEC shows high correlations with the time of day. 6. Time Series Analysis In the spherical cap harmonic analysis model, the coefficient ec 0;0 represents the average regional TEC, and the accuracy was evaluated using the data of an Australian network (ARGN) by Zahra et al. [2010] and a Chinese network by Liu et al. [2011]. Figure 8 shows the time series of the regional TEC average with 2 h resolution at four seasonal days and the immediately prior and subsequent days spring equinox (days 79 81), summer solstice (days ), autumnal equinox (days ), and winter solstice (days ) under active (2002) and calm (2008) ionosphere conditions. The regional TEC average levels at the four seasonal days are related to the solar radiation of the Arctic. At the spring equinox in 2002, the ionosphere level is higher than the value at the summer solstice, which is most likely caused by the higher solar activity level, as shown in Figure 3. LIU ET AL American Geophysical Union. All Rights Reserved. 607

8 Figure 4. Spatial distribution of mapping residuals of 12 2 h sections under active ionosphere conditions (December 2002). The color bar has a unit of TECU. The magenta lines in each subplot indicate the longitudes where local times are 12 and 14 h at the middle of the 2 h section of the corresponding subplot. The results in Figure 8 also show that the regional TEC average of the Arctic region has a lower amplitude of diurnal variation than does the middle latitude region [Liu et al., 2011]. Within the Arctic, this trend is also apparent in Figures 9 12, which show the ionosphere TEC values of different seasons at four locations of different latitudes (60 N, 70 N, 80 N, and 90 N) and longitudes (0 E, 90 E, 180 E, and 90 W). In all seasons, at a given longitude, the diurnal variation amplitude of the ionospheric TEC is lower at higher latitude where the location is closer to the North Pole. For different seasons, the diurnal variation amplitudes of the ionospheric TEC are higher in March and September than in June and December because part of the Arctic region experiences the polar day and polar night in June and December, LIU ET AL American Geophysical Union. All Rights Reserved. 608

9 Figure 5. Spatial distribution of mapping residuals of 12 2 h sections under calm ionosphere conditions (December 2008). The color bar has a unit of TECU. The magenta lines in each subplot indicate the longitudes where local times are 12 and 14 h at the middle of the 2 h section of the corresponding subplot. respectively. The results of other time points show similar results, and this trend is maintained under various ionosphere conditions. 7. Frequency Domain Analysis and Ionosphere Prediction Spherical cap harmonic analysis model has a prediction capability for future TEC because the estimated model coefficients have coherent spectrum parameters in frequency domain with ionosphere TEC. This is a significant advantage of the spherical cap harmonic analysis model comparing to the conventional regional models. In this study, we present the spectrum analysis of the time series of the estimated model coefficients. Based on the frequency domain spectrum parameters, the prediction in short and long terms is operated with the method of least squares collocation. The fast Fourier transform technique is used to analyze the frequency spectrum of the time series of the estimated model coefficients. Figure 13 shows the various period components of the time series of the model coefficient C0,0 which represents the regional TEC average. The primary components in the frequency domain include a component of years with an amplitude of 2.2 TECU, an annual component with an LIU ET AL American Geophysical Union. All Rights Reserved. 609

10 Figure 6. Spatial distribution of the Arctic ionosphere TEC of 12 2 h sections under active ionosphere conditions (22 December 2002). The color bar has a unit of TECU. The magenta lines in each subplot indicate the longitudes where local times are 12 and 14 h at the middle of the 2 h section of the corresponding subplot. amplitude of 2.58 TECU, a semiannual component with an amplitude of 1.21 TECU, a monthly 27 days component with an amplitude of 0.98 TECU, a diurnal component with an amplitude of 2.63 TECU, and a semidiurnal component with an amplitude of 0.78 TECU. These components are related to the well-known geophysics and ionosphere phenomena. The 11.2 year component is typically related to solar activity cycles. LIU ET AL American Geophysical Union. All Rights Reserved. 610

11 Figure 7. Spatial distribution of the Arctic ionosphere TEC of 12 2 h sections under calm ionosphere conditions (22 December 2008). The color bar has a unit of TECU. The magenta lines in each subplot indicate the longitudes where local times are 12 and 14 h at the middle of the 2 h section of the corresponding subplot. For the annual component, it is associated with solar ionization flux, which generally exhibits annual variations of 6 7% on a global scale and exhibits a maximum in December and minimum in June due to changes in the F2 layer electron density and the distance between the Sun and Earth. The daily component corresponds to the Earth s rotation and the period of the hour angle of the Sun. All of these components indicate LIU ET AL American Geophysical Union. All Rights Reserved. 611

12 Figure 8. The time series of the C0,0 coefficient with 2 h resolution at spring equinox, summer solstice, autumnal equinox, and winter solstice under (top) active ionosphere condition (2002) and (bottom) calm ionosphere condition (2008). that the solar radiation has strong impact on regional ionosphere activity. The semiannual component is related to the common fact that the time series of Arctic average TEC values has two local peaks during a 1 year period, as shown in Figure 15. The first peak is observed commonly in the middle of May, and the second appears around autumnal equinox. These TEC observations in the Arctic are slightly different from that in the midlatitude (e.g., China) and global areas [Liu et al., 2011; Schaer, 1999], where the two peaks usually occur in April and October. These semiannual variations are caused by the temperature of the neutrosphere and the thickness of the neutral components O and N 2 in the ionosphere [Schaer, 1999]. It should be noted that there are more spectral peaks in Figure 13, such as the 5.6 year and 9 year periods with amplitudes of over 1 TECU. These spectral peaks are not related to any well-known physics processes. Data set of a longer span and other instruments are needed to confirm and interpret these spectral peaks. Other model coefficients have significant frequency domain spectrum components of short periods, typically including semidiurnal, diurnal, monthly, semiannual, and annual components with different Figure 9. Ionosphere TEC values at four locations at different latitudes along the longitude of 0 E for 4 months in 2002: March, June, September, and December. LIU ET AL American Geophysical Union. All Rights Reserved. 612

13 Figure 10. Ionosphere TEC values at four locations at different latitudes along longitude of 90 E for 4 months in 2002: March, June, September, and December. amplitudes [Liu et al., 2008a]. Figure 14 shows the frequency spectrum of the coefficients C1,0 and S1,1 of which the most significant periodical component is the diurnal component. Based on the spectral analysis, the coefficients of the spherical cap harmonic analysis model can be predicted using the least squares collocation method [Schaer, 1999]. Therefore, a regional TEC model can be predicted, and TEC values at a given time and location can be forecasted with the predicted model. TEC prediction can be conducted over the short and long terms. The method of least squares collocation represents a time series with three components: trend function, signal, and noise. Trend function is the deterministic component of the time series, while signal is the stochastic component. The trend function for each coefficient has the form of harmonic function, which uses the periodical components obtained from the spectral analysis. Schaer [1999] and Liu et al. [2011] have presented the mathematical models for estimating the deterministic component, stochastic component, and noise as well as the corresponding covariance. Long-term TEC prediction can be performed only for the deterministic component because the autocorrelation function of the stochastic component of TEC time series drops quickly within 5 6 days [Liu et al., 2008a, Figure 11. Ionosphere TEC values at four locations at different latitudes along the longitude of 180 E for 4 months in 2002: March, June, September, and December. LIU ET AL American Geophysical Union. All Rights Reserved. 613

14 Figure 12. Ionosphere TEC values at four locations at different latitudes along the longitude of 270 E for 4 months in 2002: March, June, September, and December. 2011]. Figure 15 shows the observed regional average TEC and its trend function of the solar cycles from 2000 to 2013 and the predicted TEC for the coming 11 years from 2013 to The trend function shows the variations of the Arctic TEC in large temporal scales and the relation between seasonal variations and the solar calendar, e.g., the equinox days and the solstice days. Figure 15 shows that the Arctic ionospheric TEC has reached its latest peak at the summer of 2013, and the subsequent minimum and maximum ionosphere TEC conditions will occur in the winter of 2018 and the summer of 2024, respectively. For the latency of a solar cycle, the uncertainty of the long-term TEC prediction is 5.86 TECU with the 95% confidence level, which corresponds roughly to 75% of the maximum TEC trend. For short-term prediction, the stochastic signal component of each coefficient can also be predicted using least squares collocation. The prediction of the model can achieve a better accuracy by adding the predicted trend function to the predicted signal components for each coefficient. Figure 16 illustrates the time series of three estimated coefficients C0,0, C1,0, and S1,1 for 33 days in 2013 and their respective trend functions over the same period and the predicted coefficients for the last 3 days using the data of the previous 30 days. When all of the coefficients are predicted in the same way, TEC values at a given time and location can be predicted by using the predicted model. Figure 17 shows the predicted results at two given locations for the Figure 13. Frequency spectra of the coefficient C0,0 in the (top) long and (middle and bottom) short terms. LIU ET AL American Geophysical Union. All Rights Reserved. 614

15 Figure 14. Frequency spectra of coefficients (top) C1,0 and (bottom) S1,1. short-term scenario that predicts the SCHA models of 1, 2, and 3 days ahead by using the measurements of the previous 30 days. The prediction accuracies are ±2.2 TECU, ±3.8 TECU, and ±4.8 TECU, respectively. 8. Study Case of Tracking Ionization Patches Ionization patches are common in Arctic ionosphere, and their movement and associated density gradients have variably negative effects on high-frequency radio communications and satellite navigation and communication. Their formation and dynamics are poorly understood, particularly under disturbed space weather conditions. By referring to the result of direct observations using the SuperDARN radar network, we study the possibility of tracking ionization patches using the SCHA model, which is useful toward automatic identification and tracking of ionization patches in future. The TEC mapping of the SCHA model can represent ionospheric TEC variations related to local time and latitudes. As a study case, this section utilizes the SCHA model to track the ionization patches that occurred over the Arctic during a geomagnetic storm, which occurred on 26 September These ionization patches were directly observed by Zhang et al. using SuperDARN and GPS data. The related results were presented recently in a paper in Science [Zhang et al., 2013]. Because the SuperDARN network is sparse, and parts of areas have no TEC data available as pointed it out in Zhang et al. [2013], the observation is not continuous in the spatial domain. The TEC Figure 15. The time series of the observed regional average TEC from 2000 to 2013 and its trend function of the past solar cycle and the predicted regional average TEC for the next 11 years from 2013 to The deterministic components at four seasonal days in every year are indicated with specific symbols. LIU ET AL American Geophysical Union. All Rights Reserved. 615

16 Figure 16. The time series of the estimated coefficients (top) C0,0 (middle) C1,0 and (bottom) S1,1 for 33 days (days 170 to 203) in 2013 (in red lines); their respective trend functions for the same period (in blue lines); and the predicted coefficients for the last 3 days (in green lines) using the data of the previous 30 days, respectively. mapping of the SCHA model has full spatial coverage in the study region, and it can be used to track the evolution of the ionization patches. These results are comparable with the observations of the SuperDARN radar. By combining the knowledge of ionosphere dynamics showed in Zhang et al. [2013], Figure 18 revealed the formation and evolution of the patches using the SCHA mapping model. For the reason of comparison, the time tags for each subplot are referred to that presented in Zhang et al. [2013]. Figure 18a showed the initial condition of TEC distribution. In Figure 18b, a local TEC enhancement (ringed in black), compared to the initial condition of Figure 18a, indicated a large patch, which formed in westward of the cusp region near noon and crossed through the throat. This patch was recognized as an ionization patch in Zhang et al. [2013] by combing TEC observables and measurements of other instruments of the SuperDARN network, such as solar wind dynamic pressure and interplanetary magnetic field. The interval covered by Figures 18b and 18c represent the growth phase of the ionization patches. The patch shown in Figures 18b and 18c did not directly move across the polar cap; rather, it was stored westward of the cusp region, where it grew in size. Figure 18e showed the spatially continuous TEC mapping, which confirmed the uncertainty raised by the missing observations [Zhang et al., 2013]. In Figures 18f 18i, the patch is seen exiting the nightside auroral oval and moving sunward. Figure 17. Comparison of TEC values calculated by the estimated model and the predicted model for 3 days (days 200 to 203) in 2013 at two given locations: (top: 60 N, 24 E) and (bottom: 87.5 N, 24 E). LIU ET AL American Geophysical Union. All Rights Reserved. 616

17 Figure 18. Arctic ionospheric TEC mapping during an evolution of the ionosphere patches. The time tags of each subplot are the same as presented in Zhang et al. [2013]. The black circles and ellipses highlight the ionization patches, the evolution of which is followed in this figure. 9. Conclusions and Outlook This manuscript utilizes the spherical cap harmonic analysis method to map the Arctic ionosphere TEC during the whole period of the past solar cycle from 2000 to 2013 and analyzes the Arctic TEC over large temporal and spatial scales. The promising results show that the existing IGS stations are sufficient for mapping arctic TEC using the SCHA method with a mapping accuracy of 5 TECU for solar active periods and 2 TECU for solar calm periods. Compared to the traditional ionosphere TEC models, the SCHA model has the best mapping accuracy and reliability for the entire Arctic area under the various ionosphere conditions during a period of more than one solar cycle. The consistent mapping accuracy and reliability provides a sound basis for further analyzing the Arctic TEC and its temporal and spatial variations using the SCHA model. The study case of 26 September 2011 shows that the SCHA method presents adequate temporal and spatial resolutions to track some ionization patches in the polar region, and it is a potentially effective observation resource to complement the SuperDARN radar network, of which the observation is sparse and insufficient for some areas. LIU ET AL American Geophysical Union. All Rights Reserved. 617

18 The frequency spectrum analysis shows that the coefficients of the SCHA model have period parameters consistent with the ionosphere TEC, which provides the SCHA method with a prediction capability for future TEC. In the long term, this method predicts the deterministic component of the regional average TEC with a relative precision of more than 75% for the latency of a solar cycle of 11.2 years. For the short-term intervals, all of the model coefficients are predicted for the both deterministic and stochastic components. The predicted models are then used to predict the TEC value of a specific time and location. The prediction accuracies are ±2.2 TECU, ±3.8 TECU, and ±4.8 TECU for the cases of 1, 2, and 3 days in advance, respectively. Precise knowledge about Arctic ionosphere TEC and its variations has scientific relevance because the polar ionosphere is unique in physics. This knowledge is also important for developing precise positioning and navigation solutions for the Arctic, which are required by increasing human activities in this area, because the ionosphere is one of the main error sources in GNSS positioning. The SCHA method is essential to develop a real-time TEC mapping and prediction service for the entire Arctic region and to improve the current GNSS positioning performance and reliability. For example, the broadcast ionosphere models of the current GNSS constellations, which are commonly used in single-frequency receivers, will be evaluated and improved for the Arctic region. Acknowledgments The authors thank Q. Zhang at Shandong University in China and S. Schaer at the Astronomical Institute of the University of Bern for their valuable discussions and support regarding the data processing and analysis. The authors thank two anonymous reviewers for the valuable comments and recommendations. This work was supported in part by the Finnish Centre of Excellence in Laser Scanning Research (CoE-LaSR), which is granted by Academy of Finland with the project This work was also supported in part by the National Natural Science Foundation of China (grants , , and ). Robert Lysak thanks Alan Burns and Knut Jacobsen for their assistance in evaluating this paper. References Angling, M., J. Shaw, A. Shukla, and P. Cannon (2009), Development of an HF selection tool based on the electron density assimilative model near-real-time ionosphere, Radio Sci., 44, RS0A13, doi: /2008rs Aquino, M., J. F. G. Monico, A. H. Dodson, H. Marques, G. De Franceschi, L. Alfonsi, V. Romano, and M. Andreotti (2009), Improving the GNSS positioning stochastic model in the presence of ionospheric scintillation, J. Geod., 83(10), , doi: /s Bergeot, N., C. Bruyninx, P. Defraigne, S. Pireaux, J. Legrand, E. Pottiaux, and Q. Baire (2010), Impact of the Halloween 2003 ionospheric storm on kinematic GPS positioning in Europe, GPS Solutions, doi: /s Bilitza, D. (1995), Including auroral boundaries in the IRI model, Adv. Space Res., 16(1), Bilitza, D., L. A. McKinnell, B. Reinisch, and T. Fuller-Rowell (2011), The international reference ionosphere today and in the future, J. Geod., 85, , doi: /s x. Dach, R., U. Hugentobler, P. Fridez, and M. Meindl (2007), User manual of the Bernese GPS software version 5.0, Astronomical Institute, University of Bern, Bern, Switzerland. Fuller-Rowell, T., E. Araujo-Pradere, C. Minter, M. Codrescu, P. Spencer, D. Robertson, and A. Jacobsen (2006), US-TEC: A new data assimilation product from the space environment center characterizing the ionospheric total electron content using real-time GPS data, Radio Sci., 41, RS6003, doi: /2005rs Garner, T. W., T. Gaussiran, B. W. Tolman, R. B. Harris, R. S. Calfas, and H. Gallagher (2008), Total electron content measurements in ionospheric physics, Adv. Space Res., 42(4), , doi: /j.asr Georgiadou, Y. (1994), Modeling the Ionosphere for an Active Control Network of GPS Station, vol. 7, LGR-series, Delft Geodetic Computing Centre, Delft. Georgiadou, Y., and A. Kleusberg (1988), On the effect of ionospheric delay on geodetic relative GPS positioning, Manuscr. Geodaet., 13, 1 8. Ghoddousi-Fard, R., P. Héroux, D. Danskin, and D. Boteler (2011), Developing a GPS TEC mapping service over Canada, Space Weather, 9, S06D11, doi: /2010sw Haines, G. V. (1985), Spherical cap harmonic analysis, J. Geophys. Res., 90(B3), Haines, G. V. (1988), Computer programs for spherical cap harmonic analysis of potential and general fields, Comput. Geosci., 14(4), He, F., B. Zhang, J. Moen, and D. Huang (2011), A conjugate study of the polar ionospheric F2-layer and IRI-2007 at 75 ± magnetic latitude for solar minimum, Adv. Polar Sci., 22(3), , doi: /sp.j Hernandez-Pajares, M., J. Juan, J. Sanz, and D. Bilitza (2002), Combining GPS measurements and IRI model values for space weather specification, Adv. Space Res., 29(6), Hernández-Pajares, M., J. M. Juan, J. Sanz, R. Orus, A. Garcia-Rigo, J. Feltens, A. Komjathy, S. C. Schaer, and A. Krankowski (2009), The IGS VTEC maps: A reliable source of ionospheric information since 1998, J. Geod., 83, , doi: /s Jakowski, N., S. M. Stankov, and D. Klaehn (2005), Operational space weather service for GNSS precise positioning, Ann. Geophys., 23, Komjathy, A. (1997), Global ionospheric total electron content mapping using the global positioning system, PhD Dissertation, Department of Geodesy and Geomatics Engineering, Technical Report No. 188, University of New Brunswick, Frederiction, New Brunswick, Canada. Komjathy, A., R. Lagnley, and D. Bilitza (1998), Ingesting GPS-derived TEC data into the international reference ionosphere for single frequency radar altimeter ionosphere delay corrections, Adv. Space Res., 22(6), Li, J. (1993), The spectral methods in physical geodesy, Dissertation, Wuhan Technical University of Surveying and Mapping, Wuhan, Hubei, China. Liu, Z., and Y. Gao (2004), Ionospheric TEC predictions over a local area GPS reference network, GPS Solutions, 8(1), Liu, J., Z. Wang, H. Wang, and H. Zhang (2008a), Modeling regional ionosphere using GPS measurements over China by spherical cap harmonic analysis methodology, Geomat. Inf Sci. Wuhan Univ., 33(8), Liu, J., Z. Wang, H. Zhang, and W. Zhu (2008b), Comparison and consistency research of regional ionospheric TEC models based on GPS measurements, Geomat. Inf Sci. Wuhan Univ., 33(5), Liu, J., R. Chen, H. Kuusniemi, Z. Wang, H. Zhang, and J. Yang (2010), A preliminary study on mapping the regional ionospheric TEC using a spherical cap harmonic model in high latitudes and the Arctic region, J. GPS, 9(1), Liu, J., R. Chen, Z. Wang, and H. Zhang (2011), Spherical cap harmonic model for mapping and predicting regional TEC, GPS Solutions, 15, Sardon, E., A. Rius, and N. Zarraoa (1994), Estimation of the transmitter and receiver differential biases and the ionospheric total electron content from Global Positioning System observations, Radio Sci., 29(3), Schaer, S. (1999), Mapping and predicting the Earth s ionosphere using the Global Positioning System, Dissertation, University of Bern. LIU ET AL American Geophysical Union. All Rights Reserved. 618