Modeling the global NmF2 from the GNSS-derived TEC-GIMs

Authors

  • You Yu,

    1. Key Laboratory of Ionospheric Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    2. Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    3. University of Chinese Academy of Sciences, Beijing, China
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  • Weixing Wan,

    Corresponding author
    1. Key Laboratory of Ionospheric Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    • Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
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  • Biqiang Zhao,

    1. Key Laboratory of Ionospheric Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    2. Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
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  • Yiding Chen,

    1. Key Laboratory of Ionospheric Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    2. Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
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  • Bo Xiong,

    1. Key Laboratory of Ionospheric Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    2. Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    3. Department of Mathematics and Physics, North China Electric Power University, Baoding, China
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  • Libo Liu,

    1. Key Laboratory of Ionospheric Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    2. Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
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  • Jing Liu,

    1. Key Laboratory of Ionospheric Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    2. Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    3. University of Chinese Academy of Sciences, Beijing, China
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  • Zhipeng Ren,

    1. Key Laboratory of Ionospheric Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    2. Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
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  • Ming Li

    1. Key Laboratory of Ionospheric Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    2. Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
    3. University of Chinese Academy of Sciences, Beijing, China
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Corresponding author: W. Wan, Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China. (wanw@mail.iggcas.ac.cn)

Abstract

[1] Based on canonical correlation analysis (CCA), we propose a technique to map the peak electron density of the ionospheric F2-layer (NmF2) from the global observations of the total electron content (TEC). We first statistically analyze the canonical correlation between NmF2 and TEC using the NmF2 observations of the worldwide ionosonde stations and global ionospheric maps (GIMs) of TEC (TEC-GIMs) provided by the Jet Propulsion Laboratory. The obtained CCA modes consist of the CCA patterns and corresponding amplitudes, which separately reflect the short-term (e.g., diurnal variation) and long-term (e.g., annual, semiannual variations, and solar-cycle variations, etc.) tendencies of NmF2. With the obtained CCA patterns and corresponding amplitudes, we then construct two TEC-derived models of the monthly median NmF2, a single station model at Boulder (105.3°W, 40°N) and a global model. The CCA results are further compared with the observations and corresponding NmF2 predictions of the International Reference Ionosphere 2007 (IRI-07). It is found that the CCA NmF2 is in better agreement with the observations at Boulder than the IRI-07 NmF2. On the other hand, the temporal and spatial structures of NmF2 are successfully reproduced by the global model. Furthermore, the correlation coefficient (root mean square error) of the CCA NmF2 versus the observed NmF2 is relatively higher (lower) than that of IRI-07 NmF2. The CCA NmF2 from the global model is more reliable. Thus, we conclude that the CCA technique provides an effective approach to map the global NmF2 from the TEC-GIMs.

1 Introduction

[2] The F2-layer, the most ionized layer with the highest electron density in the ionospheric F region, is the principal reflecting layer for HF communications during both day and night. It is difficult to predict its variations because the complex chemical, photochemical, and dynamics processes simultaneously control this region. One of the most important parameters describing this layer is the critical frequency (foF2) or the peak electron density (NmF2; NmF2 = 1.24 × 1010 × foF22, foF2 is in MHz and NmF2 is in unit of el•m−3) of the F2-layer.

[3] To investigate foF2 or NmF2, multiple measurements have been developed using both ground-based and space-borne instruments. Extensive observations have been conducted from ground-based instruments like the ionosonde since the 1920s [e.g., Sethi et al., 2003; Hoque and Jakowski, 2011; McNamara et al., 2011; Siefring et al., 2011; Pavlov, 2012]. The widely used ionosonde vertical sounding technique provides creditable foF2 or NmF2 data with high accuracy and complete local time coverage. A global network of more than 200 ionosonde stations has been gradually developed. Recently, the space-borne observations, such as the Formosa Satellite 3/Constellation Observing System for Meteorology Ionosphere and Climate, Gravity Recovery and Climate Experiment, and Challenging Mini-Satellite Payload, revealed a wealth of information on the global morphology of foF2 or NmF2 with high resolutions in both space and time [e.g., Jakowski et al., 2002; Reigber et al., 2002; Lin et al., 2007; He et al., 2009; Pi et al., 2009; Wickert et al., 2009; Lin et al., 2010]. Owing to the virtue of their global spatial coverage, space-borne measurements are capable of providing the latitudinal and longitudinal structures of foF2 or NmF2 [e.g., He et al., 2009; Yue et al., 2012].

[4] However, each kind of measurement has its limitation. For instance, the ground-based observations provided by the available stations cannot afford to describe the complete longitudinal and latitudinal structures especially at the ocean and the alpine areas. On the other hand, the space-borne instruments suffer from the lack of continuous local time coverage over any given location.

[5] Attempting to fix those problems, significant efforts have been made to develop different ionospheric foF2 or NmF2 models of a single station [e.g., Pancheva and Mukhtarov, 1998; Wintoft and Cander, 2000; Liu et al., 2004; Gulyaeva et al., 2008; Xu et al., 2008; Brum et al., 2011; Liu et al., 2012], regional area [e.g., Krankowski et al., 2007; Yue et al., 2008], and the entire globe [e.g., Bailey et al., 1997; Huba et al., 2000; Bilitza, 2001; Oyeyemi et al., 2005; Bilitza and Reinisch, 2008; Nava et al., 2008; McKinnell and Oyeyemi, 2009; Hoque and Jakowski, 2011; Ren et al., 2012; Yue et al., 2012] during the past few decades.

[6] In this paper, we attempt to find a method to construct a global model of NmF2 from the global navigation satellite system (GNSS) TEC observations, taking advantage of the good linear relationship between them [Houminer and Soicher, 1994; Krankowski et al., 2007]. The global ionospheric maps of TEC (TEC-GIMs) are produced by several International GNSS Service centers (e.g., Jet Propulsion Laboratory (JPL)) since 1998 [Mannucci et al., 1998; Iijima et al., 1999; Orús et al., 2002, 2005; Wan et al., 2012]. A TEC-GIM gives a snapshot of TEC from a large amount of measurements observed by the global GNSS network, which consists of about 100 (doubled since 5 April 2004) GNSS receivers. Each GNSS receiver simultaneously obtains 6–12 TEC measurements over the site within about 1000 km horizontal range. Thus, about 600–2400 simultaneous measurements are provided to construct the GIM, which ensures the high resolution of the TEC-GIM in regions where the receiver stations are well distributed such as in North America, Europe, and part of Asia. In addition, as byproducts of the worldwide used GNSS measurements and the successfully developed mapping algorithms [Mannucci et al., 1998; Orús et al., 2002, 2005; Wan et al., 2012], TEC-GIMs are almost instantaneously, easily, and qualifiedly obtained. Based on the advantages mentioned above, it is possible and meaningful to construct the global ionospheric maps of NmF2 (NmF2-GIMs) driven by TEC with the same resolutions in space and time as those of TEC-GIMs.

[7] Making use of the good linear relationship between TEC and NmF2, we propose a mapping technique, canonical correlation analysis (CCA), in the attempt to reproduce the diurnal variation of NmF2 from that of TEC. This mapping technique, CCA, was first proposed by Hotelling [1936] and has been successfully developed and widely used, especially applied to geophysical and meteorological data [e.g., Xue et al., 2007, 2008] in recent years. The main purpose of CCA is to successively analyze the coupled variability of the two highly correlated parameters (x, y). This is accomplished by stepwise extracting different pairs of CCA modes whose cross-correlation is the biggest from the original parameters (x, y). When the observations of x precede those of y in time, the CCA method can statistically predict the values of y using x as a predictor [Wilks, 2011]. Thus, it is feasible to predict the variations of NmF2 from those of TEC observations.

[8] In the following sections, we first describe the data source in section 2. To demonstrate the CCA technique, a single station model of Boulder Station is constructed in section 3. Then, an attempt is made to map NmF2-GIMs in section 4. Meanwhile, comparisons of NmF2-GIMs between CCA and IRI-07 at 1400 magnetic local time (MLT) of different seasons for low/high solar activity are also presented. Finally, section 5 further discusses the validity of this modeling technique and gives the concluding remarks.

2 Data Source

[9] The present work uses the TEC-GIMs with a spatial resolution of 30° × 2.5° (longitude × latitude) and a temporal resolution of 1 h (UT, universal time), which is deduced from the TEC-GIMs (with a resolution of 5° × 2.5° × 2 h) archived at the website ftp://cddis.gsfc.nasa.gov/gps/products/ionex/ [Mannucci et al., 1998; Iijima et al., 1999]. NmF2 used in this work is derived from foF2 data set, which is downloaded from the Space Physics Interactive Data Resource (http://spidr.ngdc.noaa.gov/), National Institute of Information and Communications (http://wdc.nict.go.jp), and Ionospheric Prediction Service (http://www.ips.gov.au). This foF2 data set is obtained from more than 200 global ionosonde stations, which are denoted by blue pluses in Figure 1.

Figure 1.

Locations of the global ionosonde stations (blue pluses), the 57 ionosonde stations we chose for the global model (red circles), and the station of which NmF2 will be predicted (green circle). The solid lines in red are the magnetic latitudes and the red pluses represent the north and south magnetic poles.

[10] To construct the global model of NmF2, we choose 57 stations (red cycles in Figure 1) with long-term observations from those global ionosonde stations. The chosen stations are globally distributed at different latitudes and longitudes. Taking Boulder Station (105.3°W, 40°N) for example, we provide the monthly median values of hourly TEC interpolated from the JPL GIMs (Figure 2a) and the monthly median values of hourly NmF2 derived from ionosonde foF2 observations (Figure 2b) during the period from September 1998 to February 2012. As shown in Figure 2, TEC and NmF2 are similar in diurnal variation, seasonal variation, interannual variation, and the solar activity dependency. In addition, a simple calculation shows that the linear correlation coefficient between these two parameters reaches 0.95, indicating that they are in good linear correlation. The CCA method proposed in this paper is capable of constructing models with the temporal resolution of 1 day, while for the sake of brevity, we just demonstrate the method with the monthly median values of TEC and NmF2.

Figure 2.

(a) Monthly median values of hourly TEC interpolated from the JPL GIMs and (b) the monthly median values of hourly NmF2 derived from the ionosonde foF2 at Boulder Station (105.3°W, 40°N) during the period from September 1998 to February 2012.

3 Canonical Correlation Analysis Technique and Results

[11] To demonstrate the CCA technique, a single station model is first constructed using a data set containing monthly median values of hourly NmF2 and TEC at Boulder. The modeling concept of CCA technique will be briefly demonstrated in the following part. For more details of the CCA technique and the mathematical proofs, please refer to the works of Storch and Zwiers [2002] and Xue et al. [2007, 2008].

3.1 Canonical Correlation Analysis

[12] Considering a pair of M × N sample data matrixes X and Y, which contains M variables and N observations, i.e., X = (x1,x2, ⋯,xN), Y = (y1,y2, ⋯,yN) where, xi = (x1i,x2i, ⋯,xMi)T, yi = (y1i,y2i, ⋯,yMi)T.

[13] First, we remove the mean values from X and Y and rewrite them as math formula, math formula.

[14] Then, we find d (d = min(rank(X), rank(Y)) pairs of vectors math formula step by step (subject to math formula), such that the inner products math formula and math formula i = 1, 2, ⋯, d have the maximum correlations and they are not correlated with the first i − 1 pairs of inner products math formula. That is, for the correlation coefficients math formula, R1 > R2 > R3 > ⋯ > Rd; and for i ≠ j, math formula.

[15] Finally, we can construct the original sample matrixes X and Y as follows:

display math(1)
display math(2)

where, math formula and math formula. math formula and Fy are in the same definition [Storch and Zwiers, 2002]. The i-th columns of the matrix Fx and Fy are called the i-th pair of CCA patterns. Correspondingly, the i-th pair of vectors math formula are defined as the related CCA amplitudes. Also, the difference between the canonical correlation and the linear correlation is that the linear correlation considers one correlation between one pair of variables xi and yj at one time, while the canonical correlation simultaneously considers the correlations of the variables between X and Y, and the correlations of the variables from X / Y themselves.

[16] In the single station model of Boulder, we choose the time interval during which both TEC and NmF2 observations are available (the period with both data during September 1998 to November 2009; denoted by the subscript “TN”). The monthly median values of hourly TECTN and NmF2TN during the chosen period are analyzed using CCA method, which is introduced above,

display math(3)

where, m = 1, 2, ⋯, M are the numbers of month, and t = 1, 2, ⋯, 24 are the magnetic local time. 〈 TEC(t)〉TN and 〈NmF2(t)〉TN are the mean values of the observed TEC and NmF2, respectively. (ETk, ENk) are defined as the k-th pair of CCA patterns of TEC and NmF2, and math formula are the corresponding amplitudes. The superposition of the first few pairs of CCA patterns is usually capable of representing the main features of the original parameters. In the present work, the contribution of the first five CCA patterns of NmF2 to the NmF2 observation reaches 97.76%. Thus, we use the first five pairs of CCA patterns to reproduce the main structure of TEC and NmF2.

[17] Figures 3b–3f exemplify the first five pairs of CCA patterns of TEC (blue) and NmF2 (red) at Boulder. The CCA patterns, (ETk, ENk),  k = 1, 2, ⋯, 5., reveal different diurnal components of TEC and NmF2. For comparison, both the magnetic local time variations of the mean values of the two parameters, (〈 TEC 〉TN,〈NmF2〉TN), are provided in Figure 3a. Both of them gradually increase at sunrise (around 0500 MLT), peak around 1400 MLT and then slowly decrease with magnetic local time, which demonstrates the general diurnal variations of TEC and NmF2. It can be seen in Figures 3b–3f that the first five pairs of CCA patterns have clear physical implications in combination with the corresponding CCA amplitudes shown in Figures 4b–4f (TEC: blue pluses; NmF2: red crosses). For instance, the first pair of CCA patterns exhibit similar but wider diurnal variations to those of the mean values. On the other hand, the CCA amplitudes of the first pair of CCA patterns are larger in June than in December. This reflects the trend that the daytime ionosphere lasts longer during the summer because of the solar zenith angle effect. The second pair of CCA patterns exhibit similar diurnal variations to those of the mean values but with smaller width. The CCA amplitudes of the second pair of CCA patterns are smaller in June than in December. This reflects the winter anomaly pattern of the observed TEC and NmF2 for the second pair of CCA modes. The winter anomaly is a well-known characteristic of NmF2 being greater in winter than in summer during the daytime. However, the anomaly disappears at night, with NmF2 being greater in summer than in winter. In addition, the first pair of corresponding CCA amplitudes increase/decrease with the rising/falling solar activity index, the monthly median values of 10.7 cm solar radiation flux (F107), which is illustrated in Figure 4a. This is related to the solar activity dependencies of TEC and NmF2. By contrast, the seasonal anomalies of the second pair are modulated by the solar activity. The third pair of CCA patterns present typical midlatitude summer nighttime anomaly features of TEC and NmF2 in the low solar activity years (2004–2010). They exhibit a maximum around sunset during summer, which is possibly caused by the equatorward neutral winds because they sustain the ionospheric layer at higher altitudes where recombination is slower and sunlight lasts longer [Horvath and Essex, 2003; Lin et al., 2007; Burns et al., 2008; Thampi et al., 2009; Lin et al., 2010; He et al., 2011; Zhang et al., 2012; Zhao et al., 2013]. However, these midlatitude summer nighttime anomaly features are not obvious in the high solar activity years (1998–2003). This may be related to the significant influence of the solar activity, involving the semiannual variations of TEC and NmF2. For the remaining CCA patterns and amplitudes, different short-term or long-term variations of the observations are not exactly decoupled.

Figure 3.

(a) Mean values and (b–f) the first five pairs of CCA patterns of TEC (blue) and NmF2 (red) at Boulder Station.

Figure 4.

(a) F107, (b–f) the first five pairs of CCA amplitudes, and (g–k) their scatter plots of Boulder Station.

[18] Besides, the magnitude and general variation of the CCA amplitudes for NmF2 (math formula) are very close to those of TEC (math formula), as shown in Figures 4b–4f. The scatter plots of each pair of amplitudes are separately elucidated in Figures 4g–4k. It is shown that the CCA amplitudes of TEC and NmF2 are closely related and the correlation coefficients reach 1.00, 0.99, 0.97, 0.94, and 0.91, respectively. This proves that the CCA amplitudes of NmF2 are approximately equal to those of TEC, i.e., math formula. This is the essential principle of the CCA technique.

3.2 Prediction

[19] Our goal is to predict monthly median of NmF2 from TEC in any time interval (TECT denoted by the subscript “T”; the period from September 1998 to February 2012) with (September 1998 to November 2009; denoted as Period A in the following part) or without (December 2009 to February 2012; denoted as Period B) the NmF2 observations. This is accomplished by the following two steps.

[20] Step 1, predict the CCA amplitudes of NmF2T (NmF2 in the same time interval as that of TECT), i.e., math formula. The CCA amplitudes of TEC (math formula; solid lines in Figures 4b–4f) are obtained by fitting the CCA patterns of TEC (ETk) to the monthly median values of hourly TEC (TECT),

display math(4)

where, N = 5. m, t, 〈 TEC(t)〉TN and ETk(t) represent the same meanings to those of equation ((3)). According to the principle of the CCA technique mentioned above, it is feasible to predict the CCA amplitudes of NmF2 using those of TEC, i.e., math formula.

[21] Step 2, further predict NmF2 in the same time interval (NmF2T) as that of TECT using the predicted CCA amplitudes (math formula) from Step 1 and the obtained CCA patterns (ENk) from the canonical correlation analysis (section 3.1),

display math(5)

3.3 Results

[22] According to equation ((5)), we predict the NmF2 of Boulder Station during two periods mentioned above (Periods A and B are divided by the red line), as illustrated in Figure 5b. For comparison, Figures 5a and 5c separately display the variations of the observed NmF2 and modeled NmF2 from IRI-07 with the International Radio Consultative Committee coefficients [Bilitza and Reinisch, 2008]. It can be seen that the magnitude and general structure of the two modeled NmF2 (both CCA and IRI-07) are in good agreement with the observations during these two periods. The diurnal variations of both the CCA and IRI-07 NmF2 are characterized by a sunrise enhancement, peaking at around 1400 MLT, followed by a slightly decrease, which is identical to that of the observed NmF2. The two modeled NmF2 also exhibit the similar seasonal variations to those of the observed NmF2. For instance, they maximize in equinoctial months and minimize in solstitial months in most years, implying the semiannual anomaly. They are relatively large/small in the high/low solar activity years, meaning the solar activity dependency of the observations is successfully reproduced. Furthermore, as shown in Figures 5b and 5c, the magnetic local time and seasonal variations predicted by the CCA NmF2 are similar to those modeled by IRI-07 even during the periods without NmF2 observations (two time intervals during Period A (January 2003 to February 2004 and August 2004 to February 2005) and Period B). On the other hand, there are subtle discrepancies between those two modeled NmF2 and the observations. For instance, the magnitude of the IRI-07 NmF2 are generally a bit smaller/larger than those of the observations during the spring/fall, especially in the high solar activity years (1999–2002). While for the CCA NmF2, the amplitudes are close to those of the observations in most years and magnetic local times, except for the overestimated values around spring in the year 2002 and underestimated values in June of the years 2006 and 2007. In conclusion, the CCA model successfully reproduces the magnetic local time variation, the seasonal variation, and the solar activity dependency of the observations, and reasonably predicts these variations even without NmF2 observations.

Figure 5.

Monthly median values of (a) observed NmF2, modeled NmF2 from (b) CCA, and (c) IRI-07 at Boulder Station.

[23] To further verify the validity of the CCA technique, Figures 6a and 6b separately show the scatter plots for the monthly median values of CCA and IRI-07 NmF2 versus the observations. In addition, the distribution of errors between the observed NmF2 and the two modeled NmF2 are separately demonstrated in Figures 6c and 6d. The scatter plots and the histograms of Period A and B are individually illuminated in blue and green. As seen in Figures 6a and 6b, the two modeled NmF2 and the observations show a high linearity during both periods. However, IRI-07 underestimates the observations when the NmF2 are relatively large during Period A and B. A simple calculation shows that their correlation coefficients (R) between the two modeled values (CCA and IRI-07) and the observations are 0.99 and 0.97 during both periods. Meanwhile, the root mean square errors (RMSEs) between the modeled results and the observed values are individually 0.05 × 1012/0.06 × 1012 el•m−3 and 0.11 × 1012/0.07 × 1012 el•m−3 for CCA model and IRI-07 during Period A/B. Obviously, the CCA NmF2 is a quite good proxy for the structure of the observed NmF2 with higher precision.

Figure 6.

Scatter plots for the monthly median values of observed NmF2 versus modeled NmF2 ((a) CCA and (b) IRI-07) and histograms of errors between the observed NmF2 and modeled NmF2 ((c) CCA and (d) IRI-07) and observations at Boulder Station during Period A (blue) and B (green).

4 Mapping Global NmF2

[24] Because the validity of the CCA technique is verified, we then extrapolate this process to the entire globe using the global NmF2 observations (57 stations chosen in Figure 1; red circles) and TEC-GIMs. We first analyze the data set, which consists of the observed NmF2 and the interpolated TEC from the JPL TEC-GIMs at the chosen 57 ionosonde stations during September 1998 to February 2012 using the CCA technique. Similar to the single station model mentioned above, we obtain a few pairs of CCA patterns and amplitudes of TEC and NmF2. The first five pairs of CCA patterns, whose contribution can reach 97.20%, are chosen to construct the global model of NmF2. Fitting these five CCA patterns of TEC to the monthly median values of hourly TEC at each grid point of the TEC-GIMs, we further obtain the corresponding five global amplitudes. Then, the NmF2-GIMs can be constructed with the CCA patterns and the global amplitudes of TEC obtained above.

[25] As a result, the CCA NmF2-GIMs at 1400 MLT in different seasons (March (top row), June (second), September (third), and December (bottom)) at high solar activity (year 2000) and low solar activity (year 2006) are separately exemplified in the second columns of Figures 7 and 8. For the sake of brevity, just the NmF2-GIMs at 1400 MLT are exemplified in this paper. According to these figures, NmF2 are generally larger at high solar activity than that at low solar activity, which is similar to the NmF2 observations [Richards, 2001; Liu et al., 2006; Chen et al., 2008; Chen and Liu, 2010]. Furthermore, it is obvious that the NmF2 are higher in the equinoctial months (March and September) with more distinctive equatorial ionization anomaly (EIA) than in solstitial months (June and December), which is associated with the semiannual anomaly. The NmF2 in December is seen to be larger than that in June, representing the annual anomaly of the NmF2. Besides, the structures of the Northern Hemisphere and the Southern Hemisphere are not absolutely symmetric. Apparently, the NmF2-GIMs from CCA reproduce the typical features of NmF2 quite well. For comparison, the first and third columns of Figures 7 and 8 separately display the TEC-GIMs and IRI-07 NmF2 at the same time. It can be found that the global structure, the seasonal variation, and the solar activity dependency of the NmF2-GIMs are similar to those of TEC-GIMs. There also exist subtle discrepancies. On the other hand, the magnitude and main structure of the NmF2-GIMs from CCA are analogous with those of IRI-07 NmF2. However, some differences exist between them. For instance, the IRI-07 NmF2 is slightly smaller/larger than CCA NmF2 in the high/low solar activity year, especially for the crests of EIA. The EIA troughs of the NmF2 from the IRI-07 results are much wider than those from the CCA results. There are some spreading features at low latitudes in the American longitude sector especially during solar maximum in the CCA NmF2-GIMs. These features may be associated with the misleading of the JPL TEC-GIMs. We can see that the TEC-GIMs (in Figures 7 and 8) show the same spreading features in the same area. While according to the TEC observations of TOPEX during 1200–1800 MLT at different solar levels for four seasons illustrated by Jee et al. [2010], these spreading features do not exist.

Figure 7.

TEC-GIMs (the left column) at 1400 MLT provided by JPL, NmF2-GIMs modeled by CCA (middle) and IRI-07 (right) of March (top row), June (second), September (third), and December (bottom) in 2000.

Figure 8.

Same as Figure 7 but for the year 2006.

5 Discussion and Conclusion

[26] To evaluate the validity of the global NmF2 model, Figures 9a–9d demonstrate the longitude and latitude distributions of the relative RMSEs (RMSE of the relative errors between the model results and the observations) of CCA and IRI-07 at the 57 stations given in Figure 1. The distributions of the relative RMSEs for CCA (the left column) and IRI (right) models are depicted during both daytime (0800–1800 MLT; the top row) and nighttime (0100–0700 MLT and 1900–2400 MLT; bottom). It can be seen that the relative RMSEs of both models at most stations are lower than 30% and 40% (except the equatorial and low-latitude stations) during daytime and nighttime, respectively. Both models successfully reproduce the observed NmF2 at most stations. On the other hand, the relative RMSEs during daytime are relatively smaller than those during nighttime. At most stations, the relative RMSEs of CCA NmF2 are slightly smaller than those of IRI-07 NmF2 during both daytime and nighttime. Sample calculation shows that the correlation coefficient between the CCA NmF2 (0.96) and the observed NmF2 is slightly higher than that of IRI-07 (0.95), and the RMSE (0.14 × 1012 el•m−3) is lower than that of IRI-07 (0.15 × 1012 el•m−3).

Figure 9.

The longitude and latitude distributions of the relative RMSEs (RMSEs of the relative errors between the model results and the observations) of CCA (the left column) and IRI-07 (right) at the 57 stations during the daytime (the top row (a–b)) and the nighttime (bottom (c–d)).

[27] To further demonstrate the success of the mapping technique, as an example, we use the CCA patterns of the global model to predict the NmF2 of Townsville Station (146.85°E, 19.63°S, green circle in Figure 1) during September 1998 to February 2012. Figure 10 demonstrates the observed (Figure 10a), CCA (Figure 10b), and IRI-07 (Figure 10c) NmF2 of Townsville Station. We can see that the CCA NmF2 successfully reflects the main structures of the observed NmF2, such as, magnetic local time variation, seasonal variation, and the solar activity dependency. However, there are a few differences between the observations and the model results. For instance, the CCA model slightly overestimates the peak values in the years 2000 and 2002. On the other hand, IRI-07 substantially overestimates NmF2 in comparison with the CCA NmF2, which is similar to the result of Yue et al. [2012]. Moreover, the correlation coefficients between the two modeled NmF2 and the observed NmF2 are as high as 0.98 (CCA) and 0.97 (IRI-07), respectively. While the RMSEs of these two modeled NmF2 versus the observed NmF2 are 0.11 × 1012 el•m−3 and 0.15 × 1012 el•m−3, individually. Thus, the CCA model is effective with higher precision.

Figure 10.

Monthly median values of (a) observed NmF2, modeled NmF2 from (b) CCA, and (c) IRI-07 of Townsville Station (146.85°E, 19.63°S).

[28] A mapping technique, CCA method, is proposed to construct the NmF2-GIMs from the JPL TEC-GIMs in this paper. This technique provides an option for mapping NmF2 and meets with some success. If more successive foF2 data of the previous ionosonde information are included, the accuracy of the CCA modeled NmF2 will be improved. The accuracy of CCA modeled NmF2 also to some extent depends on the precision of TEC-GIMs, which would be reduced by the uncertainty resulted from the receiver differential code bias estimation, spherical symmetry assumption when converting slant TEC to vertical TEC, and interpolation during mapping. If these problems are overcome during the TEC mapping, the accuracy of CCA modeled NmF2 also can be improved. On the other hand, this mapping method is applicable to the situation that TEC and NmF2 are in good linear relationship, i.e., TEC is dominated by the NmF2 altitude area. Thus, this method might be not suitable for the exceptional situation, for instance, over the auroral region in the magnetic nighttime, or during the presunrise time.

[29] In this paper, CCA is introduced to construct the NmF2-GIMs with high resolutions in space and time from JPL TEC-GIMs during September 1998 to February 2012. First, a single station model of NmF2 at Boulder is developed to demonstrate the CCA technique. ((1)) The CCA patterns and corresponding amplitudes from the model are physically meaningful, incorporating the short-term (e.g., diurnal variation) and long-term (e.g., the solar-cycle variation, annual, semiannual variations, and the seasonal anomaly) tendencies of TEC and NmF2. ((2)) Comparison of the CCA results with the observed NmF2 proves that it is suitable to use the first five CCA patterns to reproduce the magnitude and main structures of the observations. ((3)) Further comparison with the IRI-07 NmF2 reveals that it is reasonable to use these CCA patterns to fulfill the missing data of NmF2 and predict the observations with higher accuracy.

[30] Then, an experimental model to map global NmF2 with the same resolutions of space and time as those of TEC-GIMs is constructed in the same way. ((1)) The magnitude and main structure of the CCA NmF2-GIMs are greatly analogous with those of the IRI-07 NmF2. Subtle differences exist between them. ((2)) Evaluation of the CCA and IRI-07 NmF2 at the 57 stations (from the global model) suggests that the CCA NmF2 at these stations successfully reproduce the observations with higher accuracy than those of IRI-07. ((3)) Comparison between the predictions from the global model and IRI-07 versus the observations from the ionosonde at an exemplified station, Townsville (146.85°E, 19.63°S), indicates that the correlation coefficient and RMSE between the CCA NmF2 and the observations is greater/lower than those of IRI-07.

[31] In conclusion, the CCA technique provides a reliable and effective approach to predict the monthly median of NmF2 from TEC observations. And it is worthy of further investigation.

Acknowledgments

[32] The JPL GIMs are downloaded from the web site ftp://cddis.gsfc.nasa.gov. The ionosonde foF2 data are obtained from the Space Physics Interactive Data Resource, Ionospheric Prediction Service, and National Institute of Information and Communications website. This work was supported by National Important Basic Research Project (2011CB811405), the Chinese Academy of Sciences (KZZD-EW-01-2), National Science Foundation of China (41131066, 40974090) and China Postdoctoral Science Foundation funded project (2012M520370).