Equatorial plasma bubble model for assessment of GBAS satellite availability

Abstract

One of the main concerns for Ground-Based Augmentation Systems (GBAS) is the occurrence of anomalous ionospheric conditions. In particular, ionospheric scintillation poses a significant threat, as strong scintillation events can cause GNSS receivers to lose signal lock, thereby reducing the number of available satellites for position computation. This often results in a degradation of system continuity and availability. To address this issue, this work develops a methodology to predict GBAS availability at specific airports (e.g., Tenerife Norte Airport) using a DLR-developed dynamical model of Equatorial Plasma Bubbles (EPBs), which are typically associated with scintillation events. Due to the limited number of GNSS monitoring stations surrounding Tenerife Norte Airport—a consequence of its island location and the surrounding oceanic environment—EPBs and the associated scintillation effects are simulated. The proposed approach combines reduced-order EPB modeling with a phase-gradient screen technique to reproduce scintillation generated by steep electron density gradients at EPB boundaries. By integrating these simulations with GISM-based ambient scintillation estimates and a time-varying ionospheric background model, synthetic scintillation indices are derived and subsequently used to assess DFMC GBAS availability.

1 Introduction

The Ground-Based Augmentation System (GBAS) is a local-area differential GNSS system that provides precision approach guidance for aircraft by enhancing the accuracy, integrity, and availability of GNSS signals (Radio Technical Commission for Aeronautics, 2017).

Because GBAS relies on differential corrections broadcast by a ground station, it is particularly vulnerable to so-called anomalous ionospheric gradients (Pullen et al., 2009). These gradients can introduce an undetected difference between the ionospheric delay experienced at the GBAS ground station and that experienced by the aircraft. As a result, this differential error is neither corrected through the application of pseudorange corrections nor bounded by the protection levels (PLs), which are position error bounds computed to satisfy a specified integrity risk probability.

Anomalous ionospheric gradients have traditionally been the primary concern for single-frequency single-constellation (SFSC) GBAS services, namely, GBAS Approach Service Types (GAST) C and D. Due to the limited observability of such anomalous gradients, both systems assume that worst-case ionospheric gradients—i.e., the largest gradients ever observed within the service region—are continuously present. This leads to overly conservative integrity assumptions (Pullen et al., 2009, Pullen et al., 2017).

For GAST C, which supports CAT-I operations, these conservative assumptions result in significant inflation of the ground-based integrity parameters. Consequently, the protection levels increase, reducing system availability even during periods when no anomalous gradients are actually present (Yoon et al., 2019).

In GAST D, which supports CAT-III operations, additional monitoring functions were introduced to mitigate the impact of anomalous ionospheric gradients. However, these monitors were originally designed for mid-latitude ionospheric conditions and therefore often generate false alarms when deployed in equatorial regions, where ionospheric gradients are typically stronger and frequently accompanied by scintillation phenomena (Pullen et al., 2017).

Caamano et al. (2026), Caamano et al. (2025) investigated techniques to improve availability in GAST C and GAST D by leveraging external GNSS station networks. These studies showed promising results, with significant improvements in availability in Brazil (from to ) observed even when using non-optimized networks. The results suggest that a purpose-built external GNSS monitoring network could enable GAST C to reach the availability target in equatorial regions.

With the introduction of dual-frequency, multi-constellation (DFMC) GBAS and the new GAST E architecture, the problem of anomalous gradients is largely mitigated (Murphy et al., 2022). In dual-constellation (DC) configurations, it is expected that sufficient satellites will remain usable even after discarding those affected by ionospheric gradients. This supports continued operation in the Dfree (divergence-free) mode with full availability and continuity. However, in cases where gradients extend over large areas of the sky—such as during sequences of plasma bubbles—insufficient satellites may remain for Dfree mode. In such situations, the system would switch to the ionosphere-free (Ifree) mode, which removes first-order ionospheric errors and makes the influence of gradients negligible. However, it should be noted that the Ifree mode is equally vulnerable to scintillation as the Dfree primary mode.

However, another major concern within the GAST E architecture is ionospheric scintillation, a phenomenon closely associated with anomalous ionospheric activity. Scintillation negatively affects both single-frequency single-constellation and dual-frequency multi-constellation GBAS modes through signal degradation and potential loss of satellite tracking (Aguiar et al., 2025; Costa et al., 2025). Although dual-constellation operation provides additional redundancy, equatorial regions remain particularly challenging because plasma bubbles, around which scintillation frequently occurs, often propagate in sequences, simultaneously affecting large portions of the visible sky.

This issue cannot be directly mitigated, since degraded signals must typically be excluded from processing in order to avoid corrupted measurements and potential integrity risks. Furthermore, when receiver lock on a satellite signal is lost, the corresponding satellite becomes unavailable for navigation. As a result, one of the current objectives of the GBAS community is to develop methods capable of predicting GBAS availability at specific airports based on forecasts of ionospheric storms and scintillation activity, as well as their expected impact on system performance.

To support availability prediction under such conditions, this work proposes a methodology for predicting scintillation indices based on plasma bubble modeling. The selected use case is the experimental DFMC GBAS installation at Tenerife Norte Airport. Due to the lack of a dense surrounding GNSS monitoring network in the vicinity of the airport, the plasma bubbles considered in this study were simulated.

Equatorial plasma bubbles (EPBs) are typically described using a family of models that capture their generation, structure, and evolution in the post-sunset equatorial F-region. The high-resolution EPB model of Yokoyama et al. (2014) describes equatorial plasma bubbles as large-scale depleted flux tubes generated by post-sunset generalized Rayleigh-Taylor instability, whose nonlinear evolution and rising motion are shaped by electrodynamic coupling between the E- and F-regions and by background neutral winds. Some key characteristics of synthetic scintillation associated with equatorial plasma bubbles have been derived using this model, as demonstrated in (Rino et al., 2018). The derived scintillation characteristics can be used for realistic radiowave propagation simulations through randomly inhomogeneous ionosphere with EPB signatures. However, the complexity of the model requires substantial computational resources because it solves fully coupled 3-D electrodynamic and plasma fluid equations making it significantly more computationally intensive than empirical or reduced-order EPB models such as (Rino and Carrano, 2011; Fujiwara and Tsujii, 2016; Pradipta et al., 2024; Zhao et al., 2026).

We employ one of the reduced-order EPB models introduced by Supriadi and Saito (2019) to extract the contours of the large-scale depletion structures. Because intense GNSS scintillation is widely understood to originate from multi-scale plasma irregularities localized along the steep density gradients at equatorial plasma bubble boundaries (Kintner et al., 2007; Andima et al., 2018), the modeled depletion boundaries provide a physically meaningful framework for identifying regions where severe scintillation activity is likely to occur. In this study, we apply the phase-gradient screen formalism of Vasylyev et al. (2024) to simulate scintillation produced by scattering from the sharp ionospheric density gradients that form along EPB boundaries. These simulations are combined with the Global Ionospheric Scintillation Model (GISM) (Beniguel, 2002; Vasylyev et al., 2022) scintillation-index estimation for the ambient ionosphere and incorporate the time evolution of both the EPBs and the background electron density. The resulting synthetic scintillation indices are then used to assess DFMC GBAS availability under quiet space-weather conditions.

2 Materials and methods

2.1 Feasibility of GBAS availability prediction

As mentioned in Section 1, scintillation negatively affects both both SFSC and DFMC GBAS processing modes due to signal degradation and potential loss-of-lock leads to satellite unavailability (Caamano et al., 2023). While dual-constellation operation improves robustness by providing redundancy, in equatorial regions—where plasma bubbles can occur in sequences—large portions of the visible sky may still be simultaneously affected (Fujiwara and Tsujii, 2016).

For this reason, it is desirable to develop methods capable of predicting GBAS availability at specific airports, enabling potential rerouting of aircraft in exceptional situations where ionospheric disturbances become sufficiently extensive to compromise DFMC GBAS operations, as its fallback modes (Ifree and SFMC), become unavailable.

The following sections present details on plasma bubble and scintillation simulation.

2.2 Ionospheric scintillation

The amplitude and phase of radio signals that propagate through the Earth’s ionosphere can undergo rapid fluctuations caused by the scattering of ionospheric irregularities. These irregularities distort the refractive index of the ionospheric plasma and introduce irregular deformations to the signal wavefront. Such wavefront distortions manifest as random phase fluctuations, phase scintillation, and also cause the radio wave to interfere with itself, producing amplitude scintillation (Yeh and Liu, 1982). The strength of these effects is commonly quantified by the phase scintillation index (Dierendonck et al., 1993),

and the amplitude scintillation index (Kintner et al., 2007),where is the phase of the transmitted wave, is the intensity, and is the complex amplitude of the transmitted wave. The notation denotes ensemble averaging. In the following, we focus on simulating amplitude scintillation in the low-latitude ionosphere, with particular emphasis on scattering from irregularities located at the edges of equatorial plasma bubbles.

2.3 Phase gradient screen approach

A common approach to simulating scintillation effects relies on the random phase screen method. In this framework, the split-step technique is used to solve the wave equation for an electromagnetic signal propagating through a randomly inhomogeneous medium. The medium is represented by one or several phase-modulating screens that alter only the phase of the wavefront, leaving its amplitude unchanged. The statistical properties of each screen are constructed to match the corresponding statistics of the actual randomly-inhomogeneous medium.

As the signal passes through these random phase screens, its wavefront becomes randomly corrugated, producing phase fluctuations–that is, phase scintillation–at the receiver. Between the screens, the propagation is treated as occurring in free space, so the wave evolves solely according to standard vacuum diffraction. The combination of random wavefront distortion introduced by the phase screens and the subsequent free-space diffraction leads to random modulation of the received signal power, which manifests as increased amplitude scintillation.

When strong ionospheric gradients are present, the standard phase-screen simulation method must be extended, as discussed in Vasylyev et al. (2024). In the ordinary formulation, the phase-modulating factor introduced by a phase screen is proportional to the first-order fluctuations of the electron density, which are treated as a small parameter. As a result, second-order contributions to the phase modulation are typically neglected.

However, in regions with steep ionospheric gradients, these second-order terms can become non-negligible. In such cases, the conventional phase screens no longer provide an accurate representation of the medium. They must therefore be replaced by phase-gradient screens, defined as

Hereis the ordinary phase-screen contribution for a layer of thickness located at distance from the transmitter. The coordinate system is chosen such that the -axis coincides with the propagation direction, while and denote the transverse position and gradient, respectively. The other parameters are: the signal wavelength, the classical electron radius, the fluctuating part of the electron density , and the corresponding total electron content across the layer of thickness .

The second term on the right-hand side of Equation 3 represents the phase-gradient correction. It is proportional to the scalar product of the transverse gradients of the electron-density fluctuations and the associated TEC fluctuations, and becomes significant when strong ionospheric gradients are present. In EPB-driven scintillation modeling, this correction term provides the dominant contribution to both phase and amplitude scintillation generated by scattering at the sharp electron-density gradients that form along the boundaries of plasma bubbles. These boundary regions host the strongest transverse gradients in and , making the phase-gradient term essential for accurately capturing the resulting intensity and phase fluctuations.

In the thin-phase-screen approximation (Rino, 1979), the phase and intensity of the transmitted wave can be expressed asandEquation 6 for , may be further linearized as

Here, is the phase-gradient screen defined in Equation 3, which is also ussually taken in the reduced form of Equation 4, and is the unperturbed signal intensity at the transmitter. The scintillation indices are then obtained by substituting Equations 5, 7 into Equations 1, 2, respectively.

Appendix B of Vasylyev et al. (2024) shows that the condition (or equivalently ) lead to decorrelation of the ionospheric gradients, such that Equation 8 hold true

Under these conditions, the squared scintillation indices and separate into the sum of contributions from the ordinary phase screen and from the gradient-dependent term , cf. Equation 3. These considerations suggest that the gradient-dependent term in Equation 3 can, to a good approximation, be treated as an independent phase-changing screen. In this case, the split-step wave-propagation simulation naturally separates into two parts: one using the ordinary phase screen (or multiple phase screens) , and another using the gradient-dependent phase-screen realization .

2.4 Electron density model of EPBs

The phase-gradient screen method described above relies on information about ionospheric electron-density gradients, which can be obtained from empirical datasets such as the Swarm mission’s electron-density and TEC-gradient products (Jin et al., 2022; Cahuasqui et al., 2025). However, the daily spatial coverage of these measurements in low-latitude regions is limited, making them insufficient for capturing the full range of gradient conditions relevant to equatorial plasma bubble (EPB) dynamics.

For the purposes of this study, it is more practical to derive the required gradient values using a reframed plasma-bubble model, in which the electron-density depletion associated with an EPB is embedded within a background ionospheric density distribution. This approach provides controlled, physically consistent gradient structures that can be used to derive the phase-gradient screen simulations. Here we adopt the model of Supriadi and Saito (2019), in which a plasma bubble is represented as an imposed depletion embedded within the NeQuick background electron-density field. In this formulation, the bubble is assigned a rectangular cross-section in the vertical plane aligned with the magnetic longitude.

The model introduced by Supriadi and Saito (2019) has been further adapted for wave-propagation simulations using the phase-gradient-screen method. The magnetic-equator position to align the modeled EPB structures is obtained from the IGRF-13 magnetic field model (Alken et al., 2021). Instead of simulating fully three-dimensional plasma-bubble geometries, we extract their two-dimensional contours and use these to estimate the effective ionospheric gradients along the bubble boundaries. Since the ambient electron density does not change over the irregularities scales that contribute to large ionospheric gradients, we can set as well as . Under this reduction, the scalar product of gradients in (3) becomesand the gradient-dependent term in Equation 3 can be rewritten in Equation 10Here is a scaling parameter¹ that establishes the relationship between the effective and actual gradient indices. This dimensional reduction significantly lowers computational cost and aligns naturally with the two-dimensional character of the phase-gradient screen. The resulting screen can then be superimposed onto the multiple ordinary random phase-screen simulations used in GISM.

2.5 Dynamical model of EPBs

Another key extension of the original Supriadi and Saito model is the incorporation of characteristic EPB dynamical behavior. As a first step, we include the climatological morphology of EPB occurrence following the framework of Tsunoda (1985). For each day of year (DOY) and geographic longitude, we compute the angle between the solar-terminator line and the magnetic-declination direction at the magnetic equator. The seasonal and longitudinal variation of this angle is illustrated in Figure 1. Because the growth rate of the Rayleigh-Taylor instability that drives EPB formation scales with , we adopt the criterion proposed by Tsai et al. (2024) and restrict EPB occurrence to the range , within which conditions are favorable for bubble development.

FIGURE 1

If the condition on is satisfied, the EPB model is initiated to simulate plasma-bubble formation near the solar terminator. Once generated, the bubbles are propagated eastward along the magnetic equator. The drift velocity is prescribed using the EPB model of England and Immel (2012), formulated in magnetic coordinates (Figure 2). For a given UTC time, this velocity field is transformed into geographic coordinates, as illustrated in Figure 3.

FIGURE 2

England and Immel (2012).

To assign a direction to the scalar drift speed , we determine the local orientation of the magnetic equator in geographic coordinates. Consider two infinitesimally close points on the magnetic equator with geographic coordinates and , where denotes latitude and longitude. The drift-velocity vector is then defined in Equation 11so that represents the zonal component and the meridional component of the drift. The zonal component is then corrected for Earth’s rotation, giving , where m/s is the rotational speed at the equator.

For a time elapsed since sunset, the initial EPB coordinates (in degrees) are transformed according to Equation 12where km is the Earth radius. The drift is assumed to occur at the ionospheric pierce-point altitude km. An example of EPB structures translated in this manner is shown in Figure 3a. Because the drift velocity decreases with increasing distance from the magnetic equator (see Figure 4), the translated structures bend into the characteristic banana-like shape observed as well in empirical data. We note, however, that our model does not account for other mechanisms that may contribute to the development of these characteristic shapes, see e.g., Kil et al. (2009); Karan et al. (2023).

FIGURE 3

FIGURE 4

England and Immel (2012) presented in geographical coordinates for specified universal time. The white curve represents the magnetic equator.

2.6 Model synthesis

The dynamical model of plasma bubbles summarized in Section 2.5 enables simulations of the evolution of intense scintillation arising from scattering on steep ionospheric gradients at EPB boundaries, as discussed in Section 2.3. The model depends on several input parameters, including the transmitted-signal wavelength , the ionospheric-layer thickness , the solar flux index , number of plasma bubbles , their zonal width , their bottom and top altitudes at the magnetic equator, and the distance between the consecutive bubbles. Table 1 lists typical values of several parameters, which are also used in the simulations presented in this paper.

More realistic seasonal and geographical morphology of plasma-bubble-related parameters can be incorporated by using empirical data. For example, Hei et al. (2005) examine the seasonal and regional distribution of EPB widths; Bumrungkit et al. (2018) report the typical number of observed depletion and their characteristic separation distances; and Joshi et al. (2022) present the peak-height distribution of EPBs as a function of solar flux.

The plasma-bubble contours, such as shown in Figure 3a, are used to extract the local gradient information, yielding the vector displayed in Figure 3b. Following the approach outlined at the end of Section 2.3, we simulate wave propagation through the gradient-dependent phase screen (10) using the split-step method and evaluate its contribution to the total scintillation indices. An example of this contribution to the amplitude scintillation index is presented in Figure 3c.

The GISM model is then used to simulate propagation through multiple ordinary random phase screens. The resulting total scintillation index is illustrated in Figure 3d, where the gradient-dependent scintillation from Figure 3d is superimposed on the background scintillation levels estimated by the GISM model.

The scintillation model discussed so far is applicable to the vertical propagation links. One can use simplified approach to extend its applicability to slant links. For the given link, characterized by the geographic locations of the transmitter and receiver and by the elevation and azimuth angles, we estimate the geographic coordinates of the IPP point along the link, see Supplementary Appendix 1 for details. The scintillation index for the slant link is evaluated from the vertical index at this location as given by Equation 13where we used the mapping function to project from vertical to slant direction, see e.g., (Vasylyev et al., 2022). In what follows, we use the slant scintillation index obtained with this method and omit the upper superscript for brevity.

2.7 Scintillation modeling in the context of GBAS availability

Based on the results from the previous sections, the availability of GBAS can be estimated by combining predicted scintillation index maps ( maps) with assumptions regarding receiver tracking capabilities. The goal is to estimate how many satellites remain available for positioning and how the resulting protection levels are affected. The protection levels are position error bounds computed at the required integrity risk probability and are often used to determine the availability of the system. More details can be found in Supplementary Appendix 2.

To investigate the impact of ionospheric scintillation in a realistic dynamic environment -where large-scale structures such as EPBs, which generate the scintillation, and the receiver (e.g., an aircraft) move relative to one another - we generate modeled scintillation indices as functions of geographic coordinates and time, as described in Sections 2.5, 2.6. The scintillation maps are then used together with the propagation link information corresponding to both the GBAS reference point and the user to evaluate whether the IPPs intersect equatorial plasma bubbles, thereby determining the indices affecting each satellite signal the most, cf. Section 2.6.

To implement this, we simulated the nominal 24-satellite GPS constellation and the nominal 24-satellite Galileo constellation from almanac data. The IPPs were computed for each constellation and time step for both the user and the GBAS ground station. For the user, we assumed an aircraft located at the decision height (DH) of 100 ft (CAT-II/IIIa) during one of the current CAT-I approaches into Tenerife Norte Airport. For the GBAS ground station, we simplified the scenario by placing the GBAS reference point at the location of one of the GBAS ground antennas installed at Tenerife Norte Airport. Figure 5 illustrates the relative positions of the GBAS reference point (blue) and the user (green). For each epoch, the corresponding slant value was calculated from the vertical maps at the IPP location. The corresponding IPP locations with corresponding amplitude scintillation indices are shown in Figure 6.

FIGURE 5

FIGURE 6

A threshold-based approach was applied to classify the scintillation impact. Typically, is considered strong scintillation, while indicates moderate scintillation (Jiao et al., 2013; Veettil et al., 2020; Lin et al., 2021). However, actual satellite unavailability depends strongly on design of code and carrier tracking capabilities for the respective receiver and configuration parameters. To capture this variability, two thresholds were evaluated: a robust receiver scenario, in which signal loss occurs only when , and a sensitive receiver scenario, in which loss of lock is assumed when . It should be noted that this approach does not constitute a scintillation monitoring algorithm. Instead, it provides a very simplified method to simulate receiver loss-of-lock events based on scintillation intensity represented by the index. Specifically, when the value associated with a given satellite exceeds the selected threshold (0.4 or 0.6 for sensitive and robust receivers, respectively), the corresponding signal is assumed to be certainly lost by the receiver.

Both the nominal mode Divergence-free (Dfree) and the fallback mode Ionospheric-free (Ifree) were analyzed. In this study, the main difference between the two are the values of the protection levels, which are higher for Ifree due to the higher sigmas (see Supplementary Appendix 3).

3 Results and discussion

3.1 Case 1: robust receiver and use of satellites at steady state

Figure 7a shows the number of satellites flagged by the monitor for both the GBAS ground station and the user. Each epoch in the plot corresponds to 60 s, following the resolution of the available maps. Although we assumed a transmission rate of 3 s and adapted the smoothing calculations accordingly, the results are presented only at 60-s intervals. As can be observed, the number of flagged satellites for the ground station and the user is almost identical across all epochs, with only a few exceptions. This is expected, since the ground station and user are separated by only about 3 km, and the scintillation maps have a low resolution in comparison meaning both locations typically fall within the same grid cell.

FIGURE 7

Figure 7c shows the number of visible satellites (above the elevation mask) for both the ground station (black line) and the user (orange dashed line). The counts are the same due to the short separation between the two. The magenta dot-dashed line represents the number of satellites actually used by the user. Initially, no satellites are available because the filters require a convergence time of 2 times the smoothing time constant (typically 600 s), seconds. After convergence, a maximum of 15 satellites is used, limited by the ground station’s selection. At certain times, fewer than 15 satellites are available. This occurs when a satellite in use is flagged by the ground station’s monitor, requiring the ground to substitute that satellite for another. Note that the so-called monitor is this case is not discarding satellites, but just simulating the loss of lock of the signal in the GNSS receiver if exceeds a specific value.

There are also instances where more than one satellite was flagged simultaneously, and not enough satellites were available in steady state for direct replacement. In these cases, the ground selected the next available higher-elevation satellite and waited for the filters to converge. One such example occurs around 23:30, where the number of usable satellites temporarily decreases to 12.

Figure 8c shows the Vertical Protection Level (VPL) compared with the Vertical Alert Limit (VAL) of 10 m (CAT II/III) for both the Dfree and Ifree modes. As expected, the VPL for Ifree is larger than for Dfree, since Ifree combines noise and multipath from two frequency bands, resulting in higher overall error levels. In both modes, however, the VPL remains below the VAL, owing to the favorable satellite geometry provided by dual-constellation availability. This holds true even under provided simulated scintillation conditions and with specified framework for GBAS error analysis, meaning that both availability and continuity remain at 100.

FIGURE 8

3.2 Case 2: sensitive receiver and use of satellites at steady state

Figure 7b shows the number of flagged satellites when the threshold of the monitor is lowered to 0.4, and Figure 7d shows the corresponding number of visible and usable satellites. As can be seen, when a more sensitive receiver is assumed - one that excludes satellites affected even by moderate scintillation - the number of usable satellites decreases, particularly when restricting the selection to satellites already in steady state.

This also affected the VPLs shown in Figure 8d, which are slightly larger due to the less favorable satellite geometry. Nevertheless, they remain low enough to ensure 100 availability.

3.3 Case 3: robust receiver and use of satellites during the transient phase

Figure 7e shows the number of visible and usable satellites when those considered during the transient phase of the filters (i.e., before smoothing has fully converged). In the event of a sudden loss of satellite tracking over few epochs, substituting the affected satellites with lower-elevation satellites may provide a temporary feasible strategy for the GBAS ground station. In this case, the number of usable satellites is close to 15 for almost the entire period, except at epochs where the ground had to replace satellites with others that had not been previously used. However, for the aircraft-mounted receiver, dynamic multipath effects–introduced by interactions with the aircraft hull (Felux et al., 2019), particularly the tail–may limit the usability of lower-elevation satellites. In this study, however, we neglect these effects and assume that the aircraft applies the same satellite-selection procedure as the ground station.

Including satellites during the transient phase of the filters ensures that a position solution, and thus protection levels, are available from the very beginning. However, during the first 15 min, the VPLs are noticeably larger than at later times because all satellites are still in the transient phase and their sigmas are inflated (see Figure 8e). After convergence begins, a mix of steady-state and transient-phase satellites is present. Overall, the VPL remains below the VAL at all times, thereby maintaining availability if proper filter convergence is achieved.

3.4 Case 4: sensitive receiver and use of satellites during the transient phase

Figure 7f shows the same scenario as before, but with a lower threshold applied to the S4 monitor. Since satellites in the transient phase can now also be used, the impact of signal losses is less pronounced than in Case 2, as the ground can quickly select another visible satellite for transmission. Consequently, the effect on the protection levels is minimal when comparing Cases 3 and 4 (see Figure 7f).

4 Conclusion

The developed scintillation model represents the first attempt to incorporate scintillation effects arising from scattering on EPB structures into climatological frameworks such as GISM. As with any new approach, the model has its advantages, limitations, and open challenges. The simplified plasma-bubble geometry implemented in the current framework yields computationally efficient simulations, while still producing results of sufficient fidelity for real-time applications. These characteristics make the approach appealing for operational use, particularly when compared with physics-based bubble models such as those of Rino et al. (2023), which demand substantially greater computational resources. This efficiency enables rapid evaluation of the temporal evolution of scintillation patterns, which is particularly appealing for potential forecasting applications.

One can envision a data-assimilation strategy in which empirical plasma-bubble shapes are inferred from TEC observations over Brazil. Using the propagation model, these initial structures could then be advected across the Atlantic to estimate the resulting scintillation levels at locations such as Tenerife Norte. Because EPB structures are often coherent and persist for several hours, such an approach could, in principle, provide forecasts with meaningful lead times.

However, this strategy also faces significant limitations. Most notably, it cannot account for bubble formation occurring after the solar terminator has passed beyond the Brazilian sector. Additional challenges arise from data latency: if TEC-derived bubble shapes become available only after sunrise at the target location, the bubbles may already have decayed, undermining the usefulness of the forecast. Further investigation is therefore needed to assess the practical viability of this approach and to determine under which conditions such data assimilation can yield reliable predictions.

The model itself also requires further refinement. At present, it allows only a fixed number of plasma bubbles to be generated and propagated. A more realistic approach would involve the continuous generation of bubbles as long as the solar terminator moves across the Earth and the Tsunoda conditions for EPB formation are satisfied. In addition to a more accurate formation mechanism, the model should incorporate the decay of plasma bubbles prior to local sunrise. As bubbles evolve, their shapes become increasingly diffuse, and this behavior must also be represented. Detection and monitoring algorithms for equatorial plasma bubbles - applied to both ground-based (Kriegel et al., 2017; Li et al., 2021) and satellite (Spogli et al., 2023; Christovam et al., 2026) observations - can potentially improve model performance and support more reliable nowcasting of these structures.

The model employs a simple thin-shell mapping function to project the vertical scintillation index onto an oblique slant link. This simplified treatment becomes questionable at low elevation angles, where the propagating signal may interact with irregularities distributed across multiple plasma-bubble structures rather than a single layer. To account for the altitude-dependent variation of EPB irregularity properties, one could replace the single-layer mapping approach with either a multi-layer mapping-function formulation (Hoque et al., 2025) or perform the full ray-tracing propagation calculations. Both alternatives provide a more realistic treatment of the vertical structure of the irregularities, albeit at a substantially higher computational cost.

The present study focuses on amplitude scintillation and does not address phase-scintillation effects. However, phase-induced tracking transitions can influence continuity and availability in the presence of integrity threats for GBAS operations at equatorial airports. These effects can be mitigated through non-traditional PLL architectures, such as adaptive-bandwidth techniques (e.g., Kalman-filter-based tracking), which are effective against strong phase scintillation. Such approaches are feasible for ground-based GBAS receivers. In contrast, certified airborne GNSS receivers rely on traditional PLL architectures, making phase-scintillation effects a critical issue that requires careful consideration.

Furthermore, the statistical description of plasma-bubble parameters needs improvement. For example, the model currently lacks a distribution for the spacing between bubbles, as well as a representation of bubble occurrence as a function of geographic longitude and latitude. These enhancements are planned for future iterations of the scintillation model.

Finally, from the GBAS perspective, the GAST E architecture has not yet been finalized. We are currently working on new monitors, as well as updated ground and airborne multipath models (the so-called sigmas used in this study), which are expected to slightly modify the results. In future work, we plan to repeat the analysis using these new models and monitors.

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