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Comparative analysis of two new empirical models IRI-Plas and NGM (the Neustrelitz Global Model)
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ScienceDirect Advances in Space Research 55 (2015) 2086–2098 www.elsevier.com/locate/asr
Comparative analysis of two new empirical models IRI-Plas and NGM (the Neustrelitz Global Model) O.A. Maltseva ⇑, N.S. Mozhaeva, T.V. Nikitenko Institute for Physics, Southern Federal University, Stachki, 194, Rostov-on-Don 344090, Russia Received 6 February 2014; received in revised form 22 September 2014; accepted 23 September 2014 Available online 30 September 2014
Abstract Empirical ionospheric models are under continuous development and the new model versions need to be tested and validated. In this paper two new models, the International Reference Ionosphere-Plasmasphere (IRI-Plas) and the Neustrelitz Global Model (NGM) are compared to the standard International Reference Ionosphere (IRI) in different geographical areas. Comparison is fulfilled separately for foF2, TEC, the equivalent slab thickness s. In a middle-latitude area, the foF2(NGM) model has not improved results of foF2(IRI). For subauroral areas, conditions have appeared at which foF2(NGM) provides comparable or better results than foF2(IRI). In low-latitude and equatorial areas, there are conditions when foF2(NGM) is closer to experimental data than foF2(IRI). In middle- and high-latitude areas, TEC(NGM) and TEC(IRI-Plas) provide better results, than TEC(IRI). The IRI-Plas model is better than NGM except for winter months. In low-latitude and equatorial areas, the TEC(NGM) model has shown essential advantages. The parameter s(NGM) provides in most cases the better conformity of the calculated foF2 with observational ones than s(IRI) and s(IRI-Plas). Ó 2014 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Ionosphere; Plasmasphere; Modeling; Total electron content
1. Introduction Empirical modeling is important for the study of the ionosphere and practical applications. Last years, the greatest activity is related to modeling of the total electron content (TEC). It is possible to specify two directions of this activity: (1) empirical modeling (in statistical sense), (2) models based on integration of model N(h)-profiles. Models related to the first direction are presented in papers (e.g. Kakinami et al., 2009; Jakowski et al., 2011; Mukhtarov et al., 2013). Models related to the second direction are IRI-Plas and NeQuick (Gulyaeva, 2011; Nava et al., 2008). New models need testing for revealing of conditions in which this or that model has advantages. In this paper, two models are chosen ⇑ Corresponding author.
E-mail address: [email protected] (O.A. Maltseva). http://dx.doi.org/10.1016/j.asr.2014.09.027 0273-1177/Ó 2014 COSPAR. Published by Elsevier Ltd. All rights reserved.
for comparison: IRI-Plas (Gulyaeva, 2011) and NGM (the Neustrelitz Global Model) (Jakowski et al., 2011). The NGM model is chosen because it is developed with use of new observational data (vertical sounding, radio occultation measurements) and includes not only parameter TEC, but also foF2, hmF2 (Hoque and Jakowski, 2011, 2012). It allows to determine the equivalent slab thickness of the ionosphere s(NGM) = TEC(NGM)/NmF2(NGM) and to compare it with s(IRI). The IRI-Plas model is chosen because of the updating concerning TEC calculation. It is known that models can have various accuracy level in various geographical zones, in particular, it is roughly possible to divide areas into low, middle and high latitudes. Results of comparing are given separately for these zones with usage of data of 17 stations of the vertical sounding. List of them is presented in Section 2. The purpose is to determine in what area IRI or NGM can have advantage. One
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of important TEC applications is its usage for calculation of foF2. The equivalent slab thickness s can play the important role. In paper (Maltseva et al., 2012), it is shown that the experimental thickness s(obs) allows to obtain values of foF2 closer to foF2(obs) than s(IRI), maybe, because s(IRI) is not empirical in the same sense in what TEC(IRI) is not an empirical model of TEC. In paper (Gulyaeva et al., 2013), the adaptive system of an estimation and prediction of ionospheric conditions is constructed on the basis of global TEC maps. In this system there is a calculation procedure for foF2 from current values TEC(obs). System of (Gulyaeva et al., 2013) is constructed on the basis of expression foF2 = foF2(IRI) * sqrt(TEC(obs)/TEC(IRI)). It is easy to show that value which is used in this case can be designated s(obs, IRI). It means that s(obs, IRI) is calculated from modeling values of NmF2(IRI) and observational values of TEC(obs). It differs as from s(IRI, IRI) and from s(obs, obs) which are designated s(IRI) and s(obs) for brevity. Thus, there was appeared more than one value of s: s(IRI), s(JPL), s(CODE) and others. This testifies that the empirical model of s is necessary. The purpose of this paper was to define, whether s(NGM) can fulfill a role of empirical model of s. It turns out that there are areas and levels of solar activity for which the positive answer is obtained. 2. Experimental data and models used We used the global vertical TEC maps of JPL, CODE, UPC, ESA generated by Jet Propulsion Laboratory of California Institute of Technology (JPL, Pasadena, USA, e.g. Mannucci et al., 1998), the Center for Orbit Determination in Europe (CODE, e.g. Schaer et al., 1995) of the International GPS Service for Geodynamics (Switzerland), Astronomy and Geomatics of the Polytechnical University of Catalonia, Barcelona, Spain (UPC, e.g. HernandezPajares et al., 1997), European Space Agency (ESA, Germany, Sardon et al., 1994; e.g. Jakowski et al., 1996) as a set of experimental data of the TEC values. They are extracted and calculated from the IONEX (IONosphere map Exchange) files (ftp://cddis.gsfc.nasa.gov/pub/gps/ products/ionex/) for the given coordinates and epochs. The other parameters (foF2, hmF2) were taken from the ionospheric part of the SPIDR (Space Physics Interactive Data Resource: http://spidr.ngdc.noaa.gov/spidr/ index.jsp) data base. Using these data, monthly medians have been calculated and compared to model values. Comparison have been performed by means of absolute (|DfoF2(med)|, |DTEC(med)|) deviations of model values from observational ones and relative mean square (r(foF2(med)), r(TEC(med)) deviations. In this work two models have been considered: the IRI and the NGM. In particular the IRI model has been used in two versions: IRI2001 (Bilitza, 2001) and IRI-Plas (Gulyaeva, 2011; Gulyaeva et al., 2011). One of the features of the IRI-Plas model is the inclusion of the plasmaspheric model, allowing to integrate the vertical electron density profile up to the
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required height of about 20,000 km. The IRI model was taken from the website http://ccmc.gsfc.nasa.gov/modelweb/models/iri_vitmo.php, the IRI-Plas model – from the website ftp://ftp.izmiran.rssi.ru/pub/izmiran/SPIM/. In the following, the NGM model description is given. The global model of the TEC is based on values of the CODE global map and is given by the product of five multipliers: TEC = F1 * F2 * F3 * F4 * F5. Each multiplier reflects the dependence of TEC on certain physical factors and is calculated using from 2 up to 6 coefficients. These coefficients are determined by a least squares fitting procedure superimposed on the experimental data for several years. The F1 factor describes the model dependence on the local time LT, i.e. on a solar zenith angle, and includes a daily, half-day, 8-h variations. It is calculated using 5 coefficients (C1–C5). Maximum of daily variation moved to LT = 14 as a result of 2 h delayed response of the ionosphere/thermosphere system to the daily solar excitation. The F2 factor describes the annual and semi-annual variations, using the coefficients C6–C7. The F3 factor includes the C8 coefficient describing the dependence of the TEC on the geomagnetic latitude. Coefficients C9 and C10 allow to describe the Equatorial Anomaly crests in terms of TEC. In expression F4 = 1 + C9 * exp(EC1) + C10 * exp(EC2), the first exponent refers to the northward crest of the equatorial anomaly, the second one – to the southward crest. Both exponents are functions of the geomagnetic latitude um, location of crests uC1, uC2 and their widths rC1, rC2. For TEC, these values are uC1 = 16°N, uC2 = 10°N, rC1 = 12°, rC2 = 13°. For NmF2, uC1 = 16°N, uC2 = -15°N and a specific function is used for the width rC which is the same for both crests. This factor should play a major role in the low latitudes. Coefficients C11 and C12 describe the dependence of TEC on the index F10.7: F5 = C11 + C12 * F10.7. Model for NmF2 (Hoque and Jakowski, 2011) is built on the same principle, but has 13 coefficients, since in this case the F1 factor includes 6 coefficients. The maximum of daily variation also is shifted to LT = 14. Model for hmF2 (Hoque and Jakowski, 2012) includes 4 multipliers: hmF2 = F1 * F2 * F3 * F4, because there is no special factor in relation to the equatorial anomaly description. F10.7 dependence is described by the F4 factor. Values of all coefficients were taken from corresponding papers. In the given paper the data of the following stations specified in alphabetic order was used: Ascension Island (7.9°S, 14.4°W), Athens (38°N, 23.5°E), Chilton (51.6°N, 1.3°W), Cocos (12.18°S, 96.83°E), Goosebay (53.3°N, 60.4°S), Grahamstown (33.3°S, 26.5°E), Hailsham (50.9°N, 0.34°E), Juliusruh (54.6°N, 13.38°E), Kwajalein (9°N, 167.2°E), Loparsk (68°E, 33°E), Madimbo (22.4°S, 30.9°E), Naarsarssuaq (61.2°N, 45.4°W), Niue (19.1°N, 169.9°E), Sodankyla (67.4°N, 26.6°E), Sondrestrom (67°N, 50.9°W), Thule (77.5°N, 69.2°W), Tromso (69.7°N, 19°E). Sections 3–5 of this paper provide a comparison of model-derived parameters with observational data. Discussion and conclusion are given in Section 6.
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3. Results of foF2 comparison In the IRI model arrays of standard CCIR and URSI coefficients are used. At determination of NGM coefficients the data of vertical sounding for 60 years was used, therefore it was possible to expect that values of foF2(NGM) will be closer to the experimental medians than foF2(IRI). As results depend on latitude, they are given for various latitudinal areas. We will begin with middle latitudes as for them the IRI model provides the best results. In Fig. 1, as an example the results of the Juliusruh station are given in the form of absolute deviations (upper panel) and relative standard deviations (lower panel) of the calculated values from the observed ones. It is seen that the NGM model in the majority of cases exhibits worse results than IRI. Similar results are obtained for other middle-latitude stations. For a high-altitude area, comparison examples are given in Fig. 2 for several stations and various levels of solar activity. Deviations are larger than in a middle-latitude area, though not much more. There were cases when the NGM model provides comparable or better results than the IRI model. So, for subauroral stations near to a maximum of activity (2001), it concerns to months 5–9. Near to a minimum of activity (2007), it concerns to months 2–4, 8–9. In 2010, this tendency was maintained, and the values of deviations were increased. Though a special article (Maltseva et al., 2013) is devoted to comparison of these models in low-latitude and equatorial areas, it has concerned only the small number of stations and its results need for confirmation and addition. For the Ascension Island station the following results have been obtained: in 2001 the NGM model has given comparable and best results than the IRI model, for all months, in 2003 results were comparable and in
2005 they were worse, than for IRI. In the present paper, these results are supplemented for other years (Fig. 3), and also for other stations (Fig. 4). If for the southern hemisphere station (Ascension Island) seasonal dependence is obtained: in the winter the NGM model has given the best results for low-latitude (Niue) and equatorial (Cocos, Kwajalein) stations deviations have an identical sign. For station Niue the NGM model has given the best results, than the IRI model, for station Kwajalein its results are worse, though in 2009 the NGM model has given smaller deviations for both stations. 4. Results of TEC comparison Results of TEC comparison are given for the same stations and levels of the solar activity, as in the previous Section. Results for model IRI-Plas are added. For the middlelatitude Juliusruh station, these results are presented in Fig. 5. It is seen that in most cases the IRI-Plas model provides the better results than the IRI01 model. The NGM model also yields the better results than IRI01, but a bit worse than IRI-Plas. Results for high-altitude stations are displayed in Fig. 6. Except for case of Tromso for 2007, both models improve calculation of TEC in comparison with the IRI01 model. In Fig. 7, results for the Ascension Island station and various levels of the solar activity are shown. Here, an essential advantage of the NGM model is visible. The IRI-Plas model improves results of the IRI01 model. In Fig. 8, results for low-latitude stations in 2010 are shown. Results are similar to ones of Fig. 7. It leads to a conclusion that in low-latitude and equatorial areas the NGM model performs better in terms of TEC estimation.
Fig. 1. Examples of comparison of foF2 values the for middle-latitude station, two models and various levels of the solar activity.
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Fig. 2. Examples of comparison of foF2 values for high-latitude stations, two models and various levels of the solar activity.
5. Results of s(med) comparison with experimental data The slab thickness s, defined as s = TEC/NmF2, represents the thickness of a layer in the form of a rectangle with constant density NmF2. Empirical models of s have appeared earlier than empirical models of TEC.
Calculation of TEC under formula TEC = s * NmF2 should be used having the independent empirical model of s and NmF2 from the IRI model or any another. From the previous models of s it is possible to point out s(IRI) and s(Kouris). The model s(IRI) was traditionally used for calculation of NmF2 from TEC (e.g. Gulyaeva, 2003;
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Fig. 3. Comparison of foF2 values for the Ascension is station, two models and various levels of the solar activity.
Fig. 4. Examples of comparison of foF2 values for low-latitude stations and two models in 2010.
Fig. 5. Examples of TEC comparison for the middle-latitude station, two models and various levels of the solar activity.
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Fig. 6. Examples of TEC comparison for high-altitude stations, two models and various levels of the solar activity.
Houminer and Soicher, 1996) though it is not empirical in the same sense in what the TEC(IRI) model is not empirical model of TEC. Empirical models are under construction of statistical methods. Value of TEC(IRI) is calculated as integral from a model N(h)-profile. Kouris’ model (Kouris et al., 2008, 2009) is empirical and it is
developed for the European region for midday and midnight values in the form of linear functions y = a * x + b. Coefficients a and b of these functions are given in paper (Kouris et al., 2008) in the form of tables for four years (1996, 1999, 2000, 2004). As argument of the solar activity, the moved value of a coefficient U = F10.7-66 was used.
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Fig. 7. Comparison of foF2 values for the Ascension Island station, two models and various levels of the solar activity.
Fig. 8. Examples of TEC comparison for low-latitude stations and two models in 2010.
In the paper (Maltseva et al., 2008), comparisons of TEC for various options of the IRI2007 model which has appeared at that time (corr and NeQ) with observational data of TEC-RAL have been fulfilled for the Hailsham station and three months of 2002 (September, October, November). In the paper (Maltseva et al., 2009), these results were added by comparison with TEC, calculated using s(Kouris), and also results were given for comparison of foF2(obs) values with the quantities calculated using other models of s: s(IRI2001) and s(IRI2007). In the present paper, these results are supplemented by values of TEC(NGM), TEC(IRI-Plas) and values of foF2 for s of global maps. Results are given on Fig. 9. In the left part, values of TEC(IRI-Plas) are given instead of TEC(IRI2001). On quantity, they are a bit less than TEC(IRI2001). If in a case of (Maltseva et al., 2009) the best conformity with the observational values of TEC(RAL) has been obtained for s(Kouris), now the NGM model has provided the better results than the IRI
model. Each point in the right part of Fig. 9 concerns to values of TEC corresponding to each of labels IRI, RAL, CODE for values of s corresponding to the model specified on a horizontal axis (IRI2001, IRI2007 with an option corr, IRI2007 with option NeQuick and models s(Kouris)). Both new options (IRI2007) have given better conformity with observational data, than the IRI2001model. The best conformity is obtained for the s(Kouris) model. The NGM model has shown the best result than any option of the IRI model, including the new IRI-Plas model, however it could not improve result of the s(Kouris) model. It testifies that, despite advantage of the global scale, the regional model may be better. The s(Kouris) model has appeared more reliable although it used a more simple procedure. As it is known, empirical models of ionospheric parameters give medians, i.e. characterize a mean state, close to the quiet conditions. Advantage of median s(med) is that it allows to determine foF2 from current values of TEC. These values of foF2 differ from averages and are closer
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Fig. 9. Comparison of TEC and foF2 obtained using various model s.
Fig. 10. Comparison of results of foF2 calculation using various s.
to the real data. In the paper (Maltseva et al., 2009), it is shown that the median of s allows to determine foF2 during disturbances and to fill gaps of the foF2 data. An empirical model of s is necessary for these applications. The purpose of this Section is to determine whether s(NGM) can be an empirical model of s and whether the IRI-Plas model has improved calculation of s in comparison with s(IRI). The answer is searched by means of an estimate of deviations of frequencies foF2, calculated using various s, from observational foF2(obs). These deviations are calculated for each day, therefore the label “ins” (from “instantaneous”) is used, and monthly average values are calculated. For the NGM model, values of foF2(ins) are obtained from values TEC(CODE) using s(NGM). Fig. 10 illustrate examples of comparison of critical frequencies for two global maps (“best” and “worst” from the point of view of foF2 calculation in each specific case) and two models (IRI and NGM) for middle- and two highlatitude stations in the conditions of various solar activity. The maps, satisfying to this condition, are designated by corresponding marks. In Fig. 10 the best result is provided by the JPL map, the worst one – the ESA map. It is seen that near to a maximum of activity (2001), the NGM model gives better results than the IRI model and the ESA map. In the conditions of low activity (2006) at
the middle-latitude station it provides results close to IRI. At high latitudes, it gives large deviations in winter and autumn conditions. It is worth noting that the CODE map gives the worst results in these cases. When increasing the solar activity in 2011, values of TEC increase and the NGM model again starts to give results better than the IRI model. Figs. 11 and 12 show deviations of foF2, calculated using various s for low-latitude and equatorial stations (Fig. 11 for the maximum activity, Fig. 12 for the minimum solar activity). Curves for s(CODE) and s(UPC) are not given as they are close to a curve for s(JPL). Stations are arranged for increase of an absolute value of latitude. It is seen that in most cases s(NGM) provides results better than s(IRI), however its deviations do not come nearer anywhere to the values given by s(JPL). For a minimum of activity, the NGM model has no advantages to low-latitude stations. As a whole, it is possible to note that s(NGM) may carry out a role of an empirical model. Results would be better, probably, at use of other map instead of CODE. The following problem was the estimate, whether s(IRIPlas) improves results in comparison with s(IRI), and how s(IRI-Plas) corresponds to s(obs) and s(NGM). As results depend on the solar activity and latitude, they are given for
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Fig. 11. An annual course of deviations |DfoF2(ins)| for four stations and a maximum of activity for various options s.
Fig. 12. An annual course of deviations |DfoF2(ins)| for four stations and a minimum of activity for various s.
Fig. 13. Comparison of deviations |DfoF2(ins)| of the instantaneous values foF2(ins) for a maximum of activity and various options of s.
years, close to a maximum and a minimum of activity and for several latitudinal areas. Fig. 13 shows results for a maximum, and Fig. 14 – for a minimum. For the most high-latitude Thule station, the worst results are obtained for the NGM model in a maximum and in a minimum, apparently, as consequence of small values of TEC (CODE). The IRI-Plas model improves results of the IRI model except for winter months. For high-latitude stations, results of the previous paragraph are confirmed by: improvement for the NGM model in a maximum of activity and deterioration in a minimum. The IRI-Plas model has given results, comparable with ones of the IRI model in both cases. For the middle-latitude Juliusruh station,
results for the IRI-Plas model are added in the upper drawing of Fig. 10. They are close to results of the NGM model in the maximum of the solar activity. In a minimum, the IRI-Plas model has overestimated foF2. In the low rows of Fig. 14, additional results are given for the equatorial Kwajalein station: both models NGM and IRI-Plas have improved results of IRI. Thus, at foF2 calculation from current observational values of TEC using medians of s there are conditions at which both models NGM and IRI-Plas can improve results of the IRI model however they yet have not reached level of conformity of model and observational values of foF2, peculiar to median s(med) for global maps.
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Fig. 14. Comparison of deviations |DfoF2(ins)| of the instantaneous values foF2(ins) for a minimum of activity and various options of s.
Fig. 15. Comparison of s according to radio occultation measurements and averaging for concrete stations.
Fig. 16. An illustration of unreliability of TEC calculation in the conditions of the low solar activity.
In spite of the fact that the NGM model gives good enough results, they have appeared below expectations. Probably, there are some reasons. In this paper, two reasons are considered, related to use: (1) radio occultation measurements, (2) CODE maps. In the paper (Guo et al., 2011), apparently, the first results on s are obtained using the data of radio occultation measurements and ionosondes. They concern to 2007 (an activity minimum) and are shown in Fig. 7 in paper (Guo et al., 2011) in the form of daily variations of s depending on geomagnetic latitude in a range from 60° to +60° for three seasons (winter, summer, an equinox). It is obtained that daily variations are characterized by higher values at night (from 20 LT to 06 LT) in comparison with daily ones (from 8 LT to
18 LT) in an activity minimum. In particular, in middle latitudes of the northern hemisphere values of s lie in a range from 200 km to 600 km. Daily variations of s in a summer hemisphere or in equatorial area are rather less than in a winter hemisphere. In each season a daily variation in the northern hemisphere is rather more than in the southern hemisphere. It differs from results for summer in other papers, for example (Stankov and Warnant, 2009). Pre-dawn maximums of s are accurately visible during all seasons in subauroral areas. These maximums are most expressed during winter time in northern middle latitudes between 5 LT and 6 LT. They may exceed 600 km. Pre-dawn maximums of s at middle latitudes are higher, than in equatorial and high latitudes. Also, the after-sunset
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Fig. 17. An illustration of foF2 calculation in the conditions of the low solar activity using s of various maps.
maximum was found during winter time and in an equinox between 18 LT and 20 LT though they are not so accurately expressed, as pre-dawn. In addition, there may be midday maximums during all seasons in an equatorial area with s 400 km. Every drawing gives daily variations for high latitudes for three seasons: winter (January, November, December), an equinox (February, March, April, September, October are included), summer (May–July). It was interesting to compare general results to calculations for concrete stations that can be the test for radio occultation measurements of s. Results are shown in Fig. 15. By black continuous circles results of (Guo et al., 2011) are shown, by triangle – s (CODE), as the CODE map was used for obtaining of results of (Guo et al., 2011). Results for the UPC map are in addition given. Following high- latitude stations are participated in averaging of the calculated data: Tromso, Thule, Sodankyla, Sondrestrom, and the middle-latitude Goosebay station. It is seen that in the winter and in an equinox results of two groups of measurements strongly differ on magnitude (from 2 to 6 times). Character of a daily course of s is distinguished also: the large values of TEC(UPC) provide accurately expressed features of a daily course. By results of radio occultation observations and the CODE map these features are absent. It can be related that the approach of the CODE method does not provide reliable results at low values of TEC. Additional confirmation is the behavior of TEC(CODE) shown on Fig. 16 for December 2007 when the least values are observed. For comparison, TEC are given for all maps and the IRI model. How calculation of critical frequencies foF2 can be influenced by values s for various maps, is illustrated on Fig. 17 for participating stations (high- and middlelatitudinal). It is seen that results for first (four) high-altitude stations reveal the incremented inexactness of use of s(CODE) in comparison with two (last) stations.
6. Discussion and conclusions Process of modeling of ionospheric parameters is continuous, and new models need constant testing. In this paper, it concerns to NGM and IRI-Plas models. As the standard, the IRI model serves. Comparisons with experimental data of such parameters, as foF2, TEC, s, are fulfilled. As to the model of foF2, the IRI model is considered the most reliable because any global model does not provide the better conformity to observational data than IRI. High hopes were connected with the foF2(NGM) model as it is constructed taking into account the new data on measuring Ne by method of radio occultation observations. However results have appeared not so encouraging. There are regions and conditions of the solar activity when the NGM model provides the best results but we could not envelop all regions. It is necessary to compare its results to results of the IRI model before to use the NGM model in other regions. It is possible to guess that the reason may be the discrepancy between results of radio occultation and ionosonde observations as indicated e.g. by Lin et al. (2012). Apparently, additional special effort in comparison of effects of radio occultation and ionosonde observations is necessary. As far as TEC values are concerned, there are uncertainties of their calculation because of: (1) use of the model of a thin layer, (2) constant height of this layer, (3) instrumental error due to signal delay in the transmitters and receivers. These uncertainties can be compensated at use of the relative values, but absolute values of TEC are necessary more often. Global maps of TEC give the values differing in 1.5– 2 times. Values of the CODE map are most often used, however results of TEC calculation in the conditions of a minimum of the solar activity and, especially, in a high-latitude area testify that this method has serious limitations. One of solutions here is a selection of certain value. Ionospheric and GPS communities have chosen as the standard
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the IGS value (Hernandez et al., 2009), being the robust average value according to four maps (JPL, CODE, UPC, ESA). These values can be loaded on the same site, as maps. There are first results of use of IGS values, e.g. (Lean et al., 2011). However, as it is mentioned in paper (Lastovicka, 2013), these values can have the same limitations, as well as values of separate maps. Nevertheless, it is necessary to note progress in modeling of parameter TEC: there are the models, allowing for prediction of TEC for any level of solar activity. As to the equivalent slab thickness s, its advantage consists that its median allows to obtain the instantaneous values of foF2 that is especially important for the disturbed conditions, and also that its values can be calibrated for any global map or any set of the observational values of TEC and to get current values of foF2. However sufficient attention was not given to this parameter. As to a model of s, the obtained results show that s(NGM) is modeled better than foF2(NGM) or TEC(NGM), and that there are conditions at which s(NGM) gives better results of foF2 calculation than s(IRI), however they do not come nearer to results of use of median s(obs). In this sense, it was necessary to take into account opinion of the paper (Stankov and Warnant, 2009) that for modeling s it is better to use, all the same, model N(h) – profiles. Results of use of s(IRI-Plas) show that, really, in certain cases it provides results better than s(IRI) and s(NGM), however cases of larger deviations |DfoF2(ins)| testify that the limit of improvement of the IRI model is not reached yet. Acknowledgements Authors thank scientists provided data of SPIDR, global maps of TEC, operation and modification of the IRI model, Dr M. Hoque for detailed comments concerning to the NGM model, two reviewers for very useful comments and recommendations. References Bilitza, D., 2001. International reference ionosphere 2001. Radio Sci. 36 (2), 261–275. http://dx.doi.org/10.1029/2000RS002432. Gulyaeva, T.L., 2003. International standard model of the Earth’s ionosphere and plasmasphere. Astron. Astrophys. Trans. 22 (4), 639–643. http://dx.doi.org/10.1080/10556790310001722410. Gulyaeva, T.L., 2011. Storm time behavior of topside scale height inferred from the ionosphere–plasmasphere model driven by the F2 layer peak and GPS-TEC observations. Adv. Space Res. 47, 913–920. http:// dx.doi.org/10.1016/j.asr.2010.10.025. Gulyaeva, T.L., Arikan, F., Stanislawska, I., 2011. Inter-hemispheric imaging of the ionosphere with the upgraded IRI-Plas model during the space weather storms. Earth Planets Space 63 (8), 929–939. http:// dx.doi.org/10.5047/eps.2011.04.007. Gulyaeva, T.L., Arikan, F., Hernandez-Pajares, M., Stanislawska, I., 2013. GIM-TEC adaptive ionospheric weather assessment and forecast system. J. Atmos. Sol. Terr. Phys. 102, 329–340. http://dx.doi.org/ 10.1016/j.jastp.2013.06.011. Guo, P., Xub, X., Zhang, G.X., 2011. Analysis of the ionospheric equivalent slab thickness based on ground-based GPS/TEC and GPS/
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COSMIC RO measurements. J. Atmos. Sol. Terr. Phys. 73 (7–8), 839– 846. http://dx.doi.org/10.1016/j.jastp.2011.02.002. Hernandez-Pajares, M., Juan, J.M., Sanz, J., 1997. High-resolution TEC monitoring method using permanent ground GPS receivers. Geophys. Res. Lett. 24, 1643–1646. http://dx.doi.org/10.1029/97GL01591. Hernandez-Pajares, M., Juan, J.M., Orus, R., Garcia-Rigo, A., Feltens, J., Komjathy, A., Schaer, S.C., Krankowski, A., 2009. The IGS VTEC maps: a reliable source of ionospheric information since 1998. J. Geod. 83, 263–275. http://dx.doi.org/10.1007/s00190-008-0266-1. Hoque, M.M., Jakowski, N., 2011. A new global empirical NmF2 model for operational use in radio systems. Radio Sci. 46 (RS6015), 1–13. http://dx.doi.org/10.1029/2011RS004807. Hoque, M.M., Jakowski, N., 2012. A new global model for the ionospheric F2 peak height for radio wave propagation. Ann. Geophys. 30, 797–809. http://dx.doi.org/10.5194/angeo-30-797-2012. Houminer, Z., Soicher, H., 1996. Improved short-term predictions of foF2 using GPS time delay measurements. Radio Sci. 31 (5), 1099–1108. http://dx.doi.org/10.1029/96RS01965. Jakowski, N., Sardon, E., Engler, E., Jungstand, A., Klahn, D., 1996. Relationships between GPS-signal propagation errors and EISCAT observations. Ann. Geophys. 14, 1429–1436. http://dx.doi.org/ 10.1007/s00585-996-1429-0. Jakowski, N., Hoque, M.M., Mayer, C., 2011. A new global TEC model for estimating transionospheric radio wave propagation errors. J. Geod. 85 (12), 965–974. http://dx.doi.org/10.1007/s00190-011-0455-1. Kakinami, Y., Chen, C.H., Liu, J.Y., Oyama, K.-I., Yang, W.H., Abe, S., 2009. Empirical models of total electron content based on functional fitting over Taiwan during geomagnetic quiet condition. Ann. Geophys. 27, 3321–3333. http://dx.doi.org/10.5194/angeo-27-33212009. Kouris, S.S., Polimeris, K.V., Cander, L.R., Ciraolo, L., 2008. Solar and latitude dependence of TEC and SLAB thickness. J. Atmos. Sol. Terr. Phys. 70, 1351–1365, DOI: 10.1016 /j.jastp.2008.03.009. Kouris, S.S., Polimeris, K.V., Ciraolo, L., Fotiadis, D.N., 2009. Seasonal dependence of TEC and slab thickness. Adv. Space Res. 44 (6), 715– 724. http://dx.doi.org/10.1016/j.asr.2008.10.036. Lastovicka, J., 2013. Are trends in total electron content (tec) really positive? J. Geophys. Res. Space Phys. 118, 3831–3835. http:// dx.doi.org/10.1002/jgra.50261. Lean, J., Emmert, J.T., Picone, J.M., Meier, R., 2011. Global and regional trends in ionospheric electron content. J. Geophys. Res. 116 (A2), A00H04. http://dx.doi.org/10.1029/2010JA016378. Lin, J., Wu, Y., Qiao, X., Zhou, Y., 2012. An alternative Shell inversion technique – analysis and validation based on COSMIC and ionosonde data. Adv. Space Res. 49, 89–95. http://dx.doi.org/10.1016/ j.asr.2011.08.031. Maltseva, O., Nikitenko, T., Poltavsky, O., 2008. Imitation of the IRI2007 model results for high frequency communication, XXIX General Assembly URSI, 7–16 August 2008, Chicago, USA, CD-GP1-0215, 1– 4. Maltseva, O.A., Poltavsky, O.S., Trinh, Q.T., 2009. Opportunity of the improved ionospheric model to determine radio wave propagation conditions. Electromag. Waves Electron. Syst. 6, 34–41. Maltseva, O.A., Mozhaeva, N.S., Poltavsky, O.S., Zhbankov, G.A., 2012. Use of TEC global maps and the IRI model to study ionospheric response to geomagnetic disturbances. Adv. Space Res. 49, 1076–1087. http://dx.doi.org/10.1016/j.asr.2012.01.005. Maltseva, O.A., Mozhaeva, N.S., Nikitenko, T.V., 2013. Validation of the neustrelitz global model according to the low latitude ionosphere. Adv. Space Res. 54 (3), 463–472. http://dx.doi.org/10.1016/ j.asr.2013.11.005. Mannucci, A.J., Wilson, B.D., Yuan, D.N., Ho, C.H., Lindqwister, U.J., Runge, T.F., 1998. A global mapping technique for GPS-derived ionospheric total electron content measurements. Radio Sci. 33 (3), 565–582. http://dx.doi.org/10.1029/97RS02707. Mukhtarov, P., Pancheva, D., Andonov, B., Pashova, L., 2013. Global TEC maps based on GNSS data: 1. Empirical background TEC
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model. J. Geophys. Res. Space Phys. 118, 4594–4608. http:// dx.doi.org/10.1002/jgra.50413. Nava, B., Coı¨sson, P., Radicella, S.M., 2008. A new version of the NeQuick ionospheric electron density model. J. Atmos. Sol. Terr. Phys. 70, 1856–1862. http://dx.doi.org/10.1016/j.jastp.2008.01.015. Sardon, E., Rius, A., Zarraoa, N., 1994. Estimation of the receiver differential biases and the ionospheric total electron content from global positioning system observations. Radio Sci. 29, 577–586. http:// dx.doi.org/10.1029/94RS00449.
Schaer, S., Beutler, G., Mervart, L., Rothacher, M., Wild, U., 1995. Global and regional ionosphere models using the GPS double difference phase observable, IGS Workshop, Potsdam, Germany, May 15–17, 1–16. Stankov, S.M., Warnant, R., 2009. Ionospheric slab thickness – analysis, modeling and monitoring. Adv. Space Res. 44, 1295–1303. http:// dx.doi.org/10.1016/j.asr.2009.07.010.
ScienceDirect Advances in Space Research 55 (2015) 2086–2098 www.elsevier.com/locate/asr
Comparative analysis of two new empirical models IRI-Plas and NGM (the Neustrelitz Global Model) O.A. Maltseva ⇑, N.S. Mozhaeva, T.V. Nikitenko Institute for Physics, Southern Federal University, Stachki, 194, Rostov-on-Don 344090, Russia Received 6 February 2014; received in revised form 22 September 2014; accepted 23 September 2014 Available online 30 September 2014
Abstract Empirical ionospheric models are under continuous development and the new model versions need to be tested and validated. In this paper two new models, the International Reference Ionosphere-Plasmasphere (IRI-Plas) and the Neustrelitz Global Model (NGM) are compared to the standard International Reference Ionosphere (IRI) in different geographical areas. Comparison is fulfilled separately for foF2, TEC, the equivalent slab thickness s. In a middle-latitude area, the foF2(NGM) model has not improved results of foF2(IRI). For subauroral areas, conditions have appeared at which foF2(NGM) provides comparable or better results than foF2(IRI). In low-latitude and equatorial areas, there are conditions when foF2(NGM) is closer to experimental data than foF2(IRI). In middle- and high-latitude areas, TEC(NGM) and TEC(IRI-Plas) provide better results, than TEC(IRI). The IRI-Plas model is better than NGM except for winter months. In low-latitude and equatorial areas, the TEC(NGM) model has shown essential advantages. The parameter s(NGM) provides in most cases the better conformity of the calculated foF2 with observational ones than s(IRI) and s(IRI-Plas). Ó 2014 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Ionosphere; Plasmasphere; Modeling; Total electron content
1. Introduction Empirical modeling is important for the study of the ionosphere and practical applications. Last years, the greatest activity is related to modeling of the total electron content (TEC). It is possible to specify two directions of this activity: (1) empirical modeling (in statistical sense), (2) models based on integration of model N(h)-profiles. Models related to the first direction are presented in papers (e.g. Kakinami et al., 2009; Jakowski et al., 2011; Mukhtarov et al., 2013). Models related to the second direction are IRI-Plas and NeQuick (Gulyaeva, 2011; Nava et al., 2008). New models need testing for revealing of conditions in which this or that model has advantages. In this paper, two models are chosen ⇑ Corresponding author.
E-mail address: [email protected] (O.A. Maltseva). http://dx.doi.org/10.1016/j.asr.2014.09.027 0273-1177/Ó 2014 COSPAR. Published by Elsevier Ltd. All rights reserved.
for comparison: IRI-Plas (Gulyaeva, 2011) and NGM (the Neustrelitz Global Model) (Jakowski et al., 2011). The NGM model is chosen because it is developed with use of new observational data (vertical sounding, radio occultation measurements) and includes not only parameter TEC, but also foF2, hmF2 (Hoque and Jakowski, 2011, 2012). It allows to determine the equivalent slab thickness of the ionosphere s(NGM) = TEC(NGM)/NmF2(NGM) and to compare it with s(IRI). The IRI-Plas model is chosen because of the updating concerning TEC calculation. It is known that models can have various accuracy level in various geographical zones, in particular, it is roughly possible to divide areas into low, middle and high latitudes. Results of comparing are given separately for these zones with usage of data of 17 stations of the vertical sounding. List of them is presented in Section 2. The purpose is to determine in what area IRI or NGM can have advantage. One
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of important TEC applications is its usage for calculation of foF2. The equivalent slab thickness s can play the important role. In paper (Maltseva et al., 2012), it is shown that the experimental thickness s(obs) allows to obtain values of foF2 closer to foF2(obs) than s(IRI), maybe, because s(IRI) is not empirical in the same sense in what TEC(IRI) is not an empirical model of TEC. In paper (Gulyaeva et al., 2013), the adaptive system of an estimation and prediction of ionospheric conditions is constructed on the basis of global TEC maps. In this system there is a calculation procedure for foF2 from current values TEC(obs). System of (Gulyaeva et al., 2013) is constructed on the basis of expression foF2 = foF2(IRI) * sqrt(TEC(obs)/TEC(IRI)). It is easy to show that value which is used in this case can be designated s(obs, IRI). It means that s(obs, IRI) is calculated from modeling values of NmF2(IRI) and observational values of TEC(obs). It differs as from s(IRI, IRI) and from s(obs, obs) which are designated s(IRI) and s(obs) for brevity. Thus, there was appeared more than one value of s: s(IRI), s(JPL), s(CODE) and others. This testifies that the empirical model of s is necessary. The purpose of this paper was to define, whether s(NGM) can fulfill a role of empirical model of s. It turns out that there are areas and levels of solar activity for which the positive answer is obtained. 2. Experimental data and models used We used the global vertical TEC maps of JPL, CODE, UPC, ESA generated by Jet Propulsion Laboratory of California Institute of Technology (JPL, Pasadena, USA, e.g. Mannucci et al., 1998), the Center for Orbit Determination in Europe (CODE, e.g. Schaer et al., 1995) of the International GPS Service for Geodynamics (Switzerland), Astronomy and Geomatics of the Polytechnical University of Catalonia, Barcelona, Spain (UPC, e.g. HernandezPajares et al., 1997), European Space Agency (ESA, Germany, Sardon et al., 1994; e.g. Jakowski et al., 1996) as a set of experimental data of the TEC values. They are extracted and calculated from the IONEX (IONosphere map Exchange) files (ftp://cddis.gsfc.nasa.gov/pub/gps/ products/ionex/) for the given coordinates and epochs. The other parameters (foF2, hmF2) were taken from the ionospheric part of the SPIDR (Space Physics Interactive Data Resource: http://spidr.ngdc.noaa.gov/spidr/ index.jsp) data base. Using these data, monthly medians have been calculated and compared to model values. Comparison have been performed by means of absolute (|DfoF2(med)|, |DTEC(med)|) deviations of model values from observational ones and relative mean square (r(foF2(med)), r(TEC(med)) deviations. In this work two models have been considered: the IRI and the NGM. In particular the IRI model has been used in two versions: IRI2001 (Bilitza, 2001) and IRI-Plas (Gulyaeva, 2011; Gulyaeva et al., 2011). One of the features of the IRI-Plas model is the inclusion of the plasmaspheric model, allowing to integrate the vertical electron density profile up to the
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required height of about 20,000 km. The IRI model was taken from the website http://ccmc.gsfc.nasa.gov/modelweb/models/iri_vitmo.php, the IRI-Plas model – from the website ftp://ftp.izmiran.rssi.ru/pub/izmiran/SPIM/. In the following, the NGM model description is given. The global model of the TEC is based on values of the CODE global map and is given by the product of five multipliers: TEC = F1 * F2 * F3 * F4 * F5. Each multiplier reflects the dependence of TEC on certain physical factors and is calculated using from 2 up to 6 coefficients. These coefficients are determined by a least squares fitting procedure superimposed on the experimental data for several years. The F1 factor describes the model dependence on the local time LT, i.e. on a solar zenith angle, and includes a daily, half-day, 8-h variations. It is calculated using 5 coefficients (C1–C5). Maximum of daily variation moved to LT = 14 as a result of 2 h delayed response of the ionosphere/thermosphere system to the daily solar excitation. The F2 factor describes the annual and semi-annual variations, using the coefficients C6–C7. The F3 factor includes the C8 coefficient describing the dependence of the TEC on the geomagnetic latitude. Coefficients C9 and C10 allow to describe the Equatorial Anomaly crests in terms of TEC. In expression F4 = 1 + C9 * exp(EC1) + C10 * exp(EC2), the first exponent refers to the northward crest of the equatorial anomaly, the second one – to the southward crest. Both exponents are functions of the geomagnetic latitude um, location of crests uC1, uC2 and their widths rC1, rC2. For TEC, these values are uC1 = 16°N, uC2 = 10°N, rC1 = 12°, rC2 = 13°. For NmF2, uC1 = 16°N, uC2 = -15°N and a specific function is used for the width rC which is the same for both crests. This factor should play a major role in the low latitudes. Coefficients C11 and C12 describe the dependence of TEC on the index F10.7: F5 = C11 + C12 * F10.7. Model for NmF2 (Hoque and Jakowski, 2011) is built on the same principle, but has 13 coefficients, since in this case the F1 factor includes 6 coefficients. The maximum of daily variation also is shifted to LT = 14. Model for hmF2 (Hoque and Jakowski, 2012) includes 4 multipliers: hmF2 = F1 * F2 * F3 * F4, because there is no special factor in relation to the equatorial anomaly description. F10.7 dependence is described by the F4 factor. Values of all coefficients were taken from corresponding papers. In the given paper the data of the following stations specified in alphabetic order was used: Ascension Island (7.9°S, 14.4°W), Athens (38°N, 23.5°E), Chilton (51.6°N, 1.3°W), Cocos (12.18°S, 96.83°E), Goosebay (53.3°N, 60.4°S), Grahamstown (33.3°S, 26.5°E), Hailsham (50.9°N, 0.34°E), Juliusruh (54.6°N, 13.38°E), Kwajalein (9°N, 167.2°E), Loparsk (68°E, 33°E), Madimbo (22.4°S, 30.9°E), Naarsarssuaq (61.2°N, 45.4°W), Niue (19.1°N, 169.9°E), Sodankyla (67.4°N, 26.6°E), Sondrestrom (67°N, 50.9°W), Thule (77.5°N, 69.2°W), Tromso (69.7°N, 19°E). Sections 3–5 of this paper provide a comparison of model-derived parameters with observational data. Discussion and conclusion are given in Section 6.
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3. Results of foF2 comparison In the IRI model arrays of standard CCIR and URSI coefficients are used. At determination of NGM coefficients the data of vertical sounding for 60 years was used, therefore it was possible to expect that values of foF2(NGM) will be closer to the experimental medians than foF2(IRI). As results depend on latitude, they are given for various latitudinal areas. We will begin with middle latitudes as for them the IRI model provides the best results. In Fig. 1, as an example the results of the Juliusruh station are given in the form of absolute deviations (upper panel) and relative standard deviations (lower panel) of the calculated values from the observed ones. It is seen that the NGM model in the majority of cases exhibits worse results than IRI. Similar results are obtained for other middle-latitude stations. For a high-altitude area, comparison examples are given in Fig. 2 for several stations and various levels of solar activity. Deviations are larger than in a middle-latitude area, though not much more. There were cases when the NGM model provides comparable or better results than the IRI model. So, for subauroral stations near to a maximum of activity (2001), it concerns to months 5–9. Near to a minimum of activity (2007), it concerns to months 2–4, 8–9. In 2010, this tendency was maintained, and the values of deviations were increased. Though a special article (Maltseva et al., 2013) is devoted to comparison of these models in low-latitude and equatorial areas, it has concerned only the small number of stations and its results need for confirmation and addition. For the Ascension Island station the following results have been obtained: in 2001 the NGM model has given comparable and best results than the IRI model, for all months, in 2003 results were comparable and in
2005 they were worse, than for IRI. In the present paper, these results are supplemented for other years (Fig. 3), and also for other stations (Fig. 4). If for the southern hemisphere station (Ascension Island) seasonal dependence is obtained: in the winter the NGM model has given the best results for low-latitude (Niue) and equatorial (Cocos, Kwajalein) stations deviations have an identical sign. For station Niue the NGM model has given the best results, than the IRI model, for station Kwajalein its results are worse, though in 2009 the NGM model has given smaller deviations for both stations. 4. Results of TEC comparison Results of TEC comparison are given for the same stations and levels of the solar activity, as in the previous Section. Results for model IRI-Plas are added. For the middlelatitude Juliusruh station, these results are presented in Fig. 5. It is seen that in most cases the IRI-Plas model provides the better results than the IRI01 model. The NGM model also yields the better results than IRI01, but a bit worse than IRI-Plas. Results for high-altitude stations are displayed in Fig. 6. Except for case of Tromso for 2007, both models improve calculation of TEC in comparison with the IRI01 model. In Fig. 7, results for the Ascension Island station and various levels of the solar activity are shown. Here, an essential advantage of the NGM model is visible. The IRI-Plas model improves results of the IRI01 model. In Fig. 8, results for low-latitude stations in 2010 are shown. Results are similar to ones of Fig. 7. It leads to a conclusion that in low-latitude and equatorial areas the NGM model performs better in terms of TEC estimation.
Fig. 1. Examples of comparison of foF2 values the for middle-latitude station, two models and various levels of the solar activity.
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Fig. 2. Examples of comparison of foF2 values for high-latitude stations, two models and various levels of the solar activity.
5. Results of s(med) comparison with experimental data The slab thickness s, defined as s = TEC/NmF2, represents the thickness of a layer in the form of a rectangle with constant density NmF2. Empirical models of s have appeared earlier than empirical models of TEC.
Calculation of TEC under formula TEC = s * NmF2 should be used having the independent empirical model of s and NmF2 from the IRI model or any another. From the previous models of s it is possible to point out s(IRI) and s(Kouris). The model s(IRI) was traditionally used for calculation of NmF2 from TEC (e.g. Gulyaeva, 2003;
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Fig. 3. Comparison of foF2 values for the Ascension is station, two models and various levels of the solar activity.
Fig. 4. Examples of comparison of foF2 values for low-latitude stations and two models in 2010.
Fig. 5. Examples of TEC comparison for the middle-latitude station, two models and various levels of the solar activity.
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Fig. 6. Examples of TEC comparison for high-altitude stations, two models and various levels of the solar activity.
Houminer and Soicher, 1996) though it is not empirical in the same sense in what the TEC(IRI) model is not empirical model of TEC. Empirical models are under construction of statistical methods. Value of TEC(IRI) is calculated as integral from a model N(h)-profile. Kouris’ model (Kouris et al., 2008, 2009) is empirical and it is
developed for the European region for midday and midnight values in the form of linear functions y = a * x + b. Coefficients a and b of these functions are given in paper (Kouris et al., 2008) in the form of tables for four years (1996, 1999, 2000, 2004). As argument of the solar activity, the moved value of a coefficient U = F10.7-66 was used.
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Fig. 7. Comparison of foF2 values for the Ascension Island station, two models and various levels of the solar activity.
Fig. 8. Examples of TEC comparison for low-latitude stations and two models in 2010.
In the paper (Maltseva et al., 2008), comparisons of TEC for various options of the IRI2007 model which has appeared at that time (corr and NeQ) with observational data of TEC-RAL have been fulfilled for the Hailsham station and three months of 2002 (September, October, November). In the paper (Maltseva et al., 2009), these results were added by comparison with TEC, calculated using s(Kouris), and also results were given for comparison of foF2(obs) values with the quantities calculated using other models of s: s(IRI2001) and s(IRI2007). In the present paper, these results are supplemented by values of TEC(NGM), TEC(IRI-Plas) and values of foF2 for s of global maps. Results are given on Fig. 9. In the left part, values of TEC(IRI-Plas) are given instead of TEC(IRI2001). On quantity, they are a bit less than TEC(IRI2001). If in a case of (Maltseva et al., 2009) the best conformity with the observational values of TEC(RAL) has been obtained for s(Kouris), now the NGM model has provided the better results than the IRI
model. Each point in the right part of Fig. 9 concerns to values of TEC corresponding to each of labels IRI, RAL, CODE for values of s corresponding to the model specified on a horizontal axis (IRI2001, IRI2007 with an option corr, IRI2007 with option NeQuick and models s(Kouris)). Both new options (IRI2007) have given better conformity with observational data, than the IRI2001model. The best conformity is obtained for the s(Kouris) model. The NGM model has shown the best result than any option of the IRI model, including the new IRI-Plas model, however it could not improve result of the s(Kouris) model. It testifies that, despite advantage of the global scale, the regional model may be better. The s(Kouris) model has appeared more reliable although it used a more simple procedure. As it is known, empirical models of ionospheric parameters give medians, i.e. characterize a mean state, close to the quiet conditions. Advantage of median s(med) is that it allows to determine foF2 from current values of TEC. These values of foF2 differ from averages and are closer
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Fig. 9. Comparison of TEC and foF2 obtained using various model s.
Fig. 10. Comparison of results of foF2 calculation using various s.
to the real data. In the paper (Maltseva et al., 2009), it is shown that the median of s allows to determine foF2 during disturbances and to fill gaps of the foF2 data. An empirical model of s is necessary for these applications. The purpose of this Section is to determine whether s(NGM) can be an empirical model of s and whether the IRI-Plas model has improved calculation of s in comparison with s(IRI). The answer is searched by means of an estimate of deviations of frequencies foF2, calculated using various s, from observational foF2(obs). These deviations are calculated for each day, therefore the label “ins” (from “instantaneous”) is used, and monthly average values are calculated. For the NGM model, values of foF2(ins) are obtained from values TEC(CODE) using s(NGM). Fig. 10 illustrate examples of comparison of critical frequencies for two global maps (“best” and “worst” from the point of view of foF2 calculation in each specific case) and two models (IRI and NGM) for middle- and two highlatitude stations in the conditions of various solar activity. The maps, satisfying to this condition, are designated by corresponding marks. In Fig. 10 the best result is provided by the JPL map, the worst one – the ESA map. It is seen that near to a maximum of activity (2001), the NGM model gives better results than the IRI model and the ESA map. In the conditions of low activity (2006) at
the middle-latitude station it provides results close to IRI. At high latitudes, it gives large deviations in winter and autumn conditions. It is worth noting that the CODE map gives the worst results in these cases. When increasing the solar activity in 2011, values of TEC increase and the NGM model again starts to give results better than the IRI model. Figs. 11 and 12 show deviations of foF2, calculated using various s for low-latitude and equatorial stations (Fig. 11 for the maximum activity, Fig. 12 for the minimum solar activity). Curves for s(CODE) and s(UPC) are not given as they are close to a curve for s(JPL). Stations are arranged for increase of an absolute value of latitude. It is seen that in most cases s(NGM) provides results better than s(IRI), however its deviations do not come nearer anywhere to the values given by s(JPL). For a minimum of activity, the NGM model has no advantages to low-latitude stations. As a whole, it is possible to note that s(NGM) may carry out a role of an empirical model. Results would be better, probably, at use of other map instead of CODE. The following problem was the estimate, whether s(IRIPlas) improves results in comparison with s(IRI), and how s(IRI-Plas) corresponds to s(obs) and s(NGM). As results depend on the solar activity and latitude, they are given for
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Fig. 11. An annual course of deviations |DfoF2(ins)| for four stations and a maximum of activity for various options s.
Fig. 12. An annual course of deviations |DfoF2(ins)| for four stations and a minimum of activity for various s.
Fig. 13. Comparison of deviations |DfoF2(ins)| of the instantaneous values foF2(ins) for a maximum of activity and various options of s.
years, close to a maximum and a minimum of activity and for several latitudinal areas. Fig. 13 shows results for a maximum, and Fig. 14 – for a minimum. For the most high-latitude Thule station, the worst results are obtained for the NGM model in a maximum and in a minimum, apparently, as consequence of small values of TEC (CODE). The IRI-Plas model improves results of the IRI model except for winter months. For high-latitude stations, results of the previous paragraph are confirmed by: improvement for the NGM model in a maximum of activity and deterioration in a minimum. The IRI-Plas model has given results, comparable with ones of the IRI model in both cases. For the middle-latitude Juliusruh station,
results for the IRI-Plas model are added in the upper drawing of Fig. 10. They are close to results of the NGM model in the maximum of the solar activity. In a minimum, the IRI-Plas model has overestimated foF2. In the low rows of Fig. 14, additional results are given for the equatorial Kwajalein station: both models NGM and IRI-Plas have improved results of IRI. Thus, at foF2 calculation from current observational values of TEC using medians of s there are conditions at which both models NGM and IRI-Plas can improve results of the IRI model however they yet have not reached level of conformity of model and observational values of foF2, peculiar to median s(med) for global maps.
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Fig. 14. Comparison of deviations |DfoF2(ins)| of the instantaneous values foF2(ins) for a minimum of activity and various options of s.
Fig. 15. Comparison of s according to radio occultation measurements and averaging for concrete stations.
Fig. 16. An illustration of unreliability of TEC calculation in the conditions of the low solar activity.
In spite of the fact that the NGM model gives good enough results, they have appeared below expectations. Probably, there are some reasons. In this paper, two reasons are considered, related to use: (1) radio occultation measurements, (2) CODE maps. In the paper (Guo et al., 2011), apparently, the first results on s are obtained using the data of radio occultation measurements and ionosondes. They concern to 2007 (an activity minimum) and are shown in Fig. 7 in paper (Guo et al., 2011) in the form of daily variations of s depending on geomagnetic latitude in a range from 60° to +60° for three seasons (winter, summer, an equinox). It is obtained that daily variations are characterized by higher values at night (from 20 LT to 06 LT) in comparison with daily ones (from 8 LT to
18 LT) in an activity minimum. In particular, in middle latitudes of the northern hemisphere values of s lie in a range from 200 km to 600 km. Daily variations of s in a summer hemisphere or in equatorial area are rather less than in a winter hemisphere. In each season a daily variation in the northern hemisphere is rather more than in the southern hemisphere. It differs from results for summer in other papers, for example (Stankov and Warnant, 2009). Pre-dawn maximums of s are accurately visible during all seasons in subauroral areas. These maximums are most expressed during winter time in northern middle latitudes between 5 LT and 6 LT. They may exceed 600 km. Pre-dawn maximums of s at middle latitudes are higher, than in equatorial and high latitudes. Also, the after-sunset
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Fig. 17. An illustration of foF2 calculation in the conditions of the low solar activity using s of various maps.
maximum was found during winter time and in an equinox between 18 LT and 20 LT though they are not so accurately expressed, as pre-dawn. In addition, there may be midday maximums during all seasons in an equatorial area with s 400 km. Every drawing gives daily variations for high latitudes for three seasons: winter (January, November, December), an equinox (February, March, April, September, October are included), summer (May–July). It was interesting to compare general results to calculations for concrete stations that can be the test for radio occultation measurements of s. Results are shown in Fig. 15. By black continuous circles results of (Guo et al., 2011) are shown, by triangle – s (CODE), as the CODE map was used for obtaining of results of (Guo et al., 2011). Results for the UPC map are in addition given. Following high- latitude stations are participated in averaging of the calculated data: Tromso, Thule, Sodankyla, Sondrestrom, and the middle-latitude Goosebay station. It is seen that in the winter and in an equinox results of two groups of measurements strongly differ on magnitude (from 2 to 6 times). Character of a daily course of s is distinguished also: the large values of TEC(UPC) provide accurately expressed features of a daily course. By results of radio occultation observations and the CODE map these features are absent. It can be related that the approach of the CODE method does not provide reliable results at low values of TEC. Additional confirmation is the behavior of TEC(CODE) shown on Fig. 16 for December 2007 when the least values are observed. For comparison, TEC are given for all maps and the IRI model. How calculation of critical frequencies foF2 can be influenced by values s for various maps, is illustrated on Fig. 17 for participating stations (high- and middlelatitudinal). It is seen that results for first (four) high-altitude stations reveal the incremented inexactness of use of s(CODE) in comparison with two (last) stations.
6. Discussion and conclusions Process of modeling of ionospheric parameters is continuous, and new models need constant testing. In this paper, it concerns to NGM and IRI-Plas models. As the standard, the IRI model serves. Comparisons with experimental data of such parameters, as foF2, TEC, s, are fulfilled. As to the model of foF2, the IRI model is considered the most reliable because any global model does not provide the better conformity to observational data than IRI. High hopes were connected with the foF2(NGM) model as it is constructed taking into account the new data on measuring Ne by method of radio occultation observations. However results have appeared not so encouraging. There are regions and conditions of the solar activity when the NGM model provides the best results but we could not envelop all regions. It is necessary to compare its results to results of the IRI model before to use the NGM model in other regions. It is possible to guess that the reason may be the discrepancy between results of radio occultation and ionosonde observations as indicated e.g. by Lin et al. (2012). Apparently, additional special effort in comparison of effects of radio occultation and ionosonde observations is necessary. As far as TEC values are concerned, there are uncertainties of their calculation because of: (1) use of the model of a thin layer, (2) constant height of this layer, (3) instrumental error due to signal delay in the transmitters and receivers. These uncertainties can be compensated at use of the relative values, but absolute values of TEC are necessary more often. Global maps of TEC give the values differing in 1.5– 2 times. Values of the CODE map are most often used, however results of TEC calculation in the conditions of a minimum of the solar activity and, especially, in a high-latitude area testify that this method has serious limitations. One of solutions here is a selection of certain value. Ionospheric and GPS communities have chosen as the standard
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the IGS value (Hernandez et al., 2009), being the robust average value according to four maps (JPL, CODE, UPC, ESA). These values can be loaded on the same site, as maps. There are first results of use of IGS values, e.g. (Lean et al., 2011). However, as it is mentioned in paper (Lastovicka, 2013), these values can have the same limitations, as well as values of separate maps. Nevertheless, it is necessary to note progress in modeling of parameter TEC: there are the models, allowing for prediction of TEC for any level of solar activity. As to the equivalent slab thickness s, its advantage consists that its median allows to obtain the instantaneous values of foF2 that is especially important for the disturbed conditions, and also that its values can be calibrated for any global map or any set of the observational values of TEC and to get current values of foF2. However sufficient attention was not given to this parameter. As to a model of s, the obtained results show that s(NGM) is modeled better than foF2(NGM) or TEC(NGM), and that there are conditions at which s(NGM) gives better results of foF2 calculation than s(IRI), however they do not come nearer to results of use of median s(obs). In this sense, it was necessary to take into account opinion of the paper (Stankov and Warnant, 2009) that for modeling s it is better to use, all the same, model N(h) – profiles. Results of use of s(IRI-Plas) show that, really, in certain cases it provides results better than s(IRI) and s(NGM), however cases of larger deviations |DfoF2(ins)| testify that the limit of improvement of the IRI model is not reached yet. Acknowledgements Authors thank scientists provided data of SPIDR, global maps of TEC, operation and modification of the IRI model, Dr M. Hoque for detailed comments concerning to the NGM model, two reviewers for very useful comments and recommendations. References Bilitza, D., 2001. International reference ionosphere 2001. Radio Sci. 36 (2), 261–275. http://dx.doi.org/10.1029/2000RS002432. Gulyaeva, T.L., 2003. International standard model of the Earth’s ionosphere and plasmasphere. Astron. Astrophys. Trans. 22 (4), 639–643. http://dx.doi.org/10.1080/10556790310001722410. Gulyaeva, T.L., 2011. Storm time behavior of topside scale height inferred from the ionosphere–plasmasphere model driven by the F2 layer peak and GPS-TEC observations. Adv. Space Res. 47, 913–920. http:// dx.doi.org/10.1016/j.asr.2010.10.025. Gulyaeva, T.L., Arikan, F., Stanislawska, I., 2011. Inter-hemispheric imaging of the ionosphere with the upgraded IRI-Plas model during the space weather storms. Earth Planets Space 63 (8), 929–939. http:// dx.doi.org/10.5047/eps.2011.04.007. Gulyaeva, T.L., Arikan, F., Hernandez-Pajares, M., Stanislawska, I., 2013. GIM-TEC adaptive ionospheric weather assessment and forecast system. J. Atmos. Sol. Terr. Phys. 102, 329–340. http://dx.doi.org/ 10.1016/j.jastp.2013.06.011. Guo, P., Xub, X., Zhang, G.X., 2011. Analysis of the ionospheric equivalent slab thickness based on ground-based GPS/TEC and GPS/
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