Ionospheric scintillation modeling for high- and mid-latitude using B-spline technique

Ionospheric scintillation is a phenomenon of special interest to space scientists and navigational satellite systems users. It has been widely discussed and studied in the past but, still difficult to model and predict on large scales. Ionospheric scintillations are caused due to the random electron density irregularities acting as wave scatterers (Wernik et al. 2004). As the signal propagation continues after passing through the region of irregularities in the ionosphere, phase and amplitude scintillation develops through interference of scattered rays (Kintner et al. 2007).

Climatological models are constructed to study dependencies of the strength and/or occurrence of scintillation on local time, season, solar and magnetic activity. TRANSMIT NEWSLETTER Issue 1 (2012) summarizes very briefly the important models of ionospheric scintillation that have been developed for improving GNSS vulnerability to space weather. The first empirical model of scintillation was proposed by Fremouw and Rino in 1973. This model could estimate the scintillation index \(S_{4}\) being the measure of the scintillation intensity on VHF/UHF, under weak scatter conditions roughly identified with weak scintillation. A weak scatter condition is often exceeded near the equatorial anomaly and auroral regions. This model led to the foundation of a more advanced model “WBMOD”.

Aarons developed an analytic model in 1985 using 15-min peak to peak scintillation indices (not \(S_{4}\)) taken over 5 years at Huancayo, Peru using LES 6 satellite transmitted at 254 MHz (Aarons 1985). Later came the India model by Iyer and his group in 2006 (Iyer et al. 2006). They used a cubic-B spline technique to develop an empirical model of magnetic quiet time scintillation occurrence at Indian equatorial and low latitudes. A 250 MHz signal from FLEETSAT satellite was measured for 2 years at Trivandrum, near the magnetic equator, and at Rajkot at the crest of equatorial anomaly. To describe the structure and extent of the radio scintillation generated by turbulence around and within the equatorial plumes a physical model has been developed by J.M. Retterer (2010).

The first climatological model WBMOD was developed by Northwest Research Associates, Inc. in which the user can specify his operating scenario. As the output the model returns: the phase scintillation spectral index \(p\), the spectral strength parameter \(T\), \(S_{4}\), and rms phase \(\sigma_{\varphi}\). Another, Global Ionospheric Scintillation Model (GISM), has been described by Beniguel and Buonomo in 1999. The model consists of two parts; the NeQuick model and the scintillation model based on a multiple phase screen algorithm and a second part which needs statistical information about irregularities as input. The algorithm is used to calculate the scintillation index at the receiver.

Basu and her group used in situ satellite data in scintillation modeling for the first time in 1976. They assumed a 3D power law irregularity spectrum with a constant spectral index of 4. They prepared another high latitude scintillation model (1988) using Atmospheric Explorer D data. Due to a limited availability of data the model was only suitable for northern winter under sunspot minimum condition. Wernik et al. (2007) used the Dynamics Explorer B data to estimate the irregularity spectral index and turbulence strength parameter, the factors that are required to calculate the scintillation index (Rino 1979). Their approach has been extended by Liu et al. (2012) by introducing the finite outer scale.

Models listed above reproduce well enough the global morphology of ionospheric scintillations but they often show lack of precession in detailed resolution for short time period (e.g. geophysical case studies). We will dislodge this modeling limitation by using B-spline function as a modeling tool. B-spline functions are well known for preserving the local trends of the data set even if the data is compressed on time and spatial scale. In this paper we are presenting an empirical climatological model. This model is based on the ground based GSV4004b receiver data recorded at Hornsund, Svalbard and Warsaw, Poland since 2007. We will discuss here the preparation of the data set used in this model. Great emphasis has been given to the B-spline technique used for building up the present model. For validating our model we have presented few figures equating results obtained from the model and from the observation. Results and Discussion section present and discuss seasonal and geophysical behavior of scintillation index. Conclusion section discusses merits and limitations of our model. This part is also dedicated to convince the readers of the usefulness of B-spline functions for modeling purposes.

The outcomes of the present model have been compared with other relevant models, case studies and observations. In Sect. 3 model outcomes have been discussed for Hornsund Svalbard and its similarity with the outcomes of Gola et al. (1992). In Sect. 4 our results and possible physical mechanism have been discussed along with the outcomes of many pre-existing scintillation models and case studies (e.g. Wernik et al. 2004, 2007; Coster et al. 2005; Gola et al. 1992 etc.). Such parallel discussion validates our model. Direct numerical comparison (which is mostly done in review articles) is beyond the scope of this paper since we are proposing here our model and trying to preserve the local trends of the input data using B-spline technique.

The model prepared for the Warsaw and Hornsund uses B-spline basis function of degree 4. The reason for using only 4th degree basis function is to increase the number of data points within each bin of averaged data set. B-spline is an effective technique because of full user control and there is always possibility of improvement in the model. Up to so far we have built a model in corrected geomagnetic coordinates only. Our results are in good coherence with the observation. Our results provide a clear indication of changes in scintillation morphology when we move from the mid latitude region to the high latitude region. Therefore we say here strictly that our model is validated. For Hornsund scintillation index, for the CGM latitude \((\varLambda^{\circ}) > 75^{\circ}\) is varying independently with respect to the MLT and geomagnetic activity. This may be due to large scale irregularity. The stagnant variation in scintillation pattern during equinox seems due to long life time of large scale (hundreds of meters to kilometers) irregularity and their convection from the places of origin (Aarons 1982). Ionospheric irregularities present in the high latitude ionosphere are kept in motion by phenomena that couple momentum and energy from the solar wind into the Earth’s magnetosphere. The convection of irregularities is controlled by interplanetary magnetic field (IMF) (Kelley et al. 1982). Coupling occurs where the magnetic fields of the magnetosheath and magnetosphere are antiparallel. During southward orientation of the IMF (i.e. \(B_{z-}\)), coupling occurs on the subsolar magnetopause near the noon MLT meridian. For azimuthal IMF (i.e., \(B_{y+}\) or \(B_{y-}\)), the location of coupling in the northern hemisphere shifts either towards dusk or dawn, respectively (Ruohoniemi and Greenwald 2005). While during summer most intense scintillation is observed near magnetic midnight and magnetic noon. With increasing geomagnetic activity, scintillation pattern spreads near magnetic midnight and magnetic dusk regions as evident in Fig. 3. The possible explanation for this is, during the summer, high E-region conductivity slows the instability growth rate and increases the cross-field plasma diffusion, which removes small-scale structures already at a short distance from the source (corrected geomagnetic latitudes corresponding to the magnetic midnight and magnetic noon) region (Kivanç and Heelis 1998). But in the cusp and night time auroral regions medium and large scale structures are created by structured fluxes of precipitated electrons. With increasing magnetic activity and in some situation these medium and large scale structures may produce small scale structures through the \(E \times B\) or current-convective instability (Wernik et al. 2004). For geomagnetic quiet condition during winters the scintillation index for the CGM latitude \((\varLambda^{\circ}) > 75^{\circ}\) scintillation index maximizes near magnetic noon followed by magnetic dusk and magnetic night time regions. As the magnetic activity increases, scintillation index start following MLT. During winters the convecting structures decay less rapidly and give rise to scintillation patterns. But, with increased geomagnetic activity it is possible that these decaying convecting structures may form small scale structures through \(E \times B\) instability which follow MLT (Gola et al. 1992).

For Warsaw we observed that during equinox and weak magnetic condition scintillation pattern for CGML latitude ≥50 degree are strongly dependent on MLT. But, with increasing magnetic activity scintillation pattern shows weak dependence on MLT. Main cause of scintillation at mid-latitudes is inner-magnetospheric electric field creating irregularities on pre-existing ionospheric density gradients and local instabilities operating on pre-existing ionospheric density gradients (Coster et al. 2005). With increase in geomagnetic field, regions hosting large ionospheric density gradient last longer since, they are associated with high velocity ionospheric flows. In summer we observe strongest scintillation as compared to the other seasons. During the full sunlit days of summer months, E-region conductivity increases due to photo ionization. This may contribute to the enhanced inner-magnetospheric electric fields which reveal rapidly fluctuating plasma drifts (Wernik et al. 2007). Scintillation patterns follow MLT during winter months and shows equatorward spread with magnetic field enhancement. Taking \(E \times B\) instability mechanism into account winter scintillation pattern could be explained quite satisfactorily. The \(E \times B\) instability is the only cause responsible for producing Fresnel scale irregularities (Mishin et al. 2003a, 2003b). The Poynting vector represents the directional energy flux density of an electromagnetic field. This vector can be in both directions upwards and downward. Few times the electric field can be in coherence with the density fluctuations.