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

Abstract

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.

Keywords

• 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

Abstract

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

Keywords

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

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