Regional spatio - temporal modeling of the ionospheric Vertical Total Electron Content VTEC using Multivariate Adaptive Regression B‒Splines BMARS

Öz

Spatio‒temporal Regional modeling of the ionosphere in terms of the vertical total electron content VTEC is accomplished using a non‒parametric Multivariate Adaptive Regression B‒ Spline BMARS algorithm on the basis of Global Positioning System GPS observations. The basis functions are constructed as compactly supported tensor products of quadratic B‒Splines which are derived from the observations automatically. A smooth approximation is achieved by scale‒by‒scale model building strategy which searches for best fitting B Spline to the data at each scale. The real data set processed is gathered from ground based GPS stations in Europe and falls within the time interval of the geomagnetic storm on 15 February, 2011. The result of BMARS modeling apparently demonstrates the efficiency and the potential of the method. It is also compared both numerically and visually with a well‒known global and regional VTEC modeling based on spherical harmonics and B‒Splines respectively.

Anahtar Kelimeler

• Ionosphere, GPS, MARS, B‒spline, BMARS, Regional modeling

Bölgesel iyonosferik Düşey Toplam Elektron İçeriğinin VTEC mekansal ve zamansal boyutlarda Çok Değişkenli Uyabilen B-Spline Regresyonu BMARS kullanılarak belirlenmesi

Öz

Mekansal ve zamansal bölgesel İyonosferin Düşey Toplam Elektron İçeriği VTEC cinsinden modellenmesi parametrik olmayan Çok Değişkenli Uyabilen B-Spline fonksiyonlarına Dayalı Regresyon BMARS kullanılarak gerçekleştirilmektedir. Gözlemlerden otomatik olarak üretilen Baz Fonksiyonları, karesel ikinci derece B-Spline fonksiyonlarının sıkılaştırılmış destekli tensör çarpımlarından oluşturulmaktadır. Yumuşatılmış bir yaklaştırıma sıralı ölçeklendirmeye dayalı bir model kurma stratejisiyle ulaşılmaktadır. Bu strateji veriye her ölçekte en iyi uyan B-Spline fonksiyonunu aramaktadır. İşlenen veri grubu Avrupa’ daki yersel GPS istasyonlarından toplanmış olup, 15 Şubat 2011 tarihinde meydana gelen jeomanyetik bir fırtınayı da içermektedir. BMARS modellemesinin sonucu bu yöntemin etkinliğini ve potansiyelini açıkca göstermektedir. Hesaplanan sonuç, aynı zamanda gerek nümerik gerekse görsel olarak, tanınmış küresel ve bölgesel modellerle karşılaştırılmıştır. Küresel model küresel harmonik fonksiyonlara, bölgesel model de B-Spline fonksiyonlarına dayanmaktadır

Anahtar Kelimeler

• İyonosfer, GPS, MARS, B-spline, BMARS, Bölgesel modelleme

Kaynakça

1. Bakin S., Hegland M., Osborne M., (1997), Computational techniques and applications conference: Can mars be improved with b-splines?, Computational Techniques and Applications Conference, Adelaide, Avustralya.
2. Bakin S., Hegland M., Williams G., (2000), Mining taxation data with parallel BMARS, Parallel Algorithms and Applications, 15, 37-55.
3. Brunini C., Meza A., Azpilicueta F., Zele M.A.V., (2004). A new ionosphere monitoring technology based on GPS, Astrophysics and Space Science, 290(3–4), 415–429.
4. Brunini C., Camilion E., Azpilicueta F., (2010), Assessment of SIRGAS ionospheric maps errors based on a numerical simulation, EGU General Assembly, 2-7 Mayıs, Vienna, Avusturya, s.1840
5. Cox M., (1982), Practical spline approximation, Topics in Analysis' ın İçinde, (Turner P., Ed.), Lecture Notes in Mathematics, Cilt. 965, Springer, Berlin/Heidelberg, ss.79–112.
6. Crino S., Brown D.E., (2007), Global Optimization with Multivariate Adaptive Regression Splines. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 37(2), 333–340.
7. Dettmering D., (2003), The Utilisation of The GPS For Modelling the Ionosphere in Three Dimensions, Teknik Raporlar, Report Nr. 2003.1, Doktora Tezi, Department of Geodesy and and Geoinformatics, Stuttgart Üniversitesi.
8. Durmaz M., Karslioglu M.O., Nohutcu M., (2010), Regional VTEC modeling with multivariate adaptive regression splines, Advances in Space Research, 46(2), 180–189.

9. Ekman T., Kubin G., (1999), Nonlinear prediction of mobile radio channels: measurements and mars model designs, IEEE International Conference on Acoustics Speech and Signal Processing, 5, 2667–2670.
10. Friedman J.H., (1991), Multivariate adaptive regression splines, The Annals of Statistics, 19(1), 1–67.
11. Garcia-Fernandez M., (2004), Contributions to the 3D Ionospheric Sounding with GPS Data. Doktora Tezi, Department of Applied Mathematics IV and Applied Physics, Technical University of Catalonia, Barcelona, İspanya.
12. Hernandez-Pajares M., Sanz J.M.J.J., (1999), New approaches in global ionospheric determination using ground GPS data, Journal of Atmospheric and Solar Terrestrial Physics, 61(16), 1237–1247.
13. Hofmann-Wellenhof B., Lichtenegger H., Wasle E., (2008), GNSS Global Navigation Satellite Systems GPS, GLONASS, Galileo more. Springer, Avusturya.
14. Jin S.G., Luo O., Park P., (2008), GPS observations of the ionospheric F2-Layer behaviour during the 20th November 2003 geomagnetic storm over South Korea, Journal of Geodesy, 82(12), 883–892.
15. Jin S.G., Park J., Wang J., Choi B., Park P., (2006), Electron density profiles derived from ground-based GPS observations, Journal of Navigation, 59(3), 395–401.
16. Jin S.G., Wang H.P., Zhu W.Y., (2004), Realtime prediction and monitoring of the total ionospheric electron content by means of GPS observations, Chinese Astronomy and Astrophysics, 28(3), 331–337.
17. Lewis P.A.W., Stevens J.G., (1991), Nonlinear modeling of time series using Multivariate Adaptive Regression Splines (MARS), Journal of the American Statistical Association, 86(416), 864– 877.
18. Liu Z., Gao Y., (2004), Ionospheric TEC Predictions over a local area GPS reference network, GPS Solutions, 8(1), 23–29.
19. 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 Science, 33(3), 565–582.
20. Misra P., Enge P., (2003), Global Positioning System: Signals, Measurements, and Performance. Ganga-Jamuna Press, Massachusetts, ABD.
21. Nohutcu M., Karslioglu M., Schmidt M., (2010), B-Spline modeling of VTEC over Turkey using GPS observations, Journal Of Atmospheric and Solar- Terrestrial Physics, 72(7–8), 617–624.
22. Nohutcu M., Karslioglu M.O., Gucluer B., Schmidt M., Zeilhofer C., Zhang Z., Ergintav S., (2007), Local modeling of TEC using GPS observations, TUJK Scientific Meeting Proceedings'in İçinde, Ankara, Türkiye.
23. Policy Workshop Report, (2011), Satellite Navigation & Space Weather: Understanding the Vulnerability & Building Resilience, American Meteorological Society.
24. Schaer S., (1999), Mapping and Predicting the Earth’s Ionosphere Using the Global Positioning System, Doktora Tezi, University of Bern , İsviçre.
25. Schmidt M., (2007), Wavelet modeling in support of IRI, Advances in Space Research, 39(5), 932–940.
26. Schmidt M., Bilitza D., Shum C.K., Zeilhofer C., (2007a), Regional 4-D Modeling of the ionospheric electron content, Advances in Space Research, 42(4), 782–790.
27. Schmidt M., Karslioglu M.O., Zeilhofer C., (2007b), Regional multi-dimensional modeling of the ionosphere from satellite data, TUJK Scientific Meeting Proceedings'in İçinde, Ankara, Türkiye.
28. Seeber G., (2003), Satelite Geodesy, de Gruyter, Berlin, Almanya, 589 ss.
29. Wielgosz P., Grejner-Brzezinska D.A., Kashani I., (2003), Regional ionosphere mapping with kriging and multiquadric methods, Journal of Global Positioning Systems, 2(1), 48–55.
30. Yang C.C., Prasher S.O., Lacroix R., Kim S.H., (2004), Application of Multivariate Adaptive Regression Splines (MARS) to simulate soil temperature. Transactions of the ASAE, 47(3), 881–887.
31. Yuan Y., Ou J., (2002), Differential areas for differential stations (DADS): A new method of establishing grid ionospheric model, Chinese Science Bulletin, 47(12), 1033–1036.
32. Zeilhofer C., (2008), Multi-Dimensional B-Spline Modeling of Spatio-Temporal Ionospheric Signals, German Geodetic Commission, Cilt.123, Seri A, Muenchen.