On the Occurrence of GPS Signal Amplitude Degradation for Receivers on Board LEO Satellites

Transient signal loss of the global positioning system (GPS) has been frequently observed by receivers on board the European Space Agency's Swarm mission when the satellites encounter ionospheric plasma irregularities. In this study we provided the first comparison of the GPS signal amplitude degradations from receivers on board low Earth orbiting satellites at different altitudes. Intense carrier phase variations but almost no amplitude fades (less than 2 dB Hz) are observed when the spaceborne receiver lies right inside the ionospheric plasma irregularities, like the case for the Swarm and CHAMP satellites flying at about 400–500 km. This indicates that the strong phase variation, but not the amplitude fades, causes the receivers to stop tracking the GPS signals. When the receiver is located 100–200 km below the slab of plasma irregularities, like the case for the GOCE satellite flying at about 250 km, signal amplitude fades exceeding 10 dB Hz are observed, in addition to strong phase variation. Our results suggest that a considerable distance of the receiver to the plasma irregularity slab is needed to affect the Fresnel diffractive process and further causes GPS signal amplitude fades.


Introduction
Plasma irregularities are an important subject for ionospheric studies, as they can cause disturbances of the transionospheric radio wave signals. When propagating through Earth's ionosphere, the radio waves interact with free electrons along the transmission paths, introducing group delay and phase advance (Kintner et al., 2007). When the radio waves strike a volume of plasma irregularities, rapid fluctuations of the carrier phase and amplitude are usually observed from ground-based receivers, which is also called ionospheric scintillations. With the development of global navigation satellite systems (GNSS) in the past decades, scintillation on the L-band frequency has been widely investigated (e.g., Aarons, 1982;Aarons & Basu, 1994;Basu et al., 1980;Bhattacharyya et al., 2014;Kintner et al., 2007). From a global view, ionospheric scintillations are most frequently observed at the equatorial and low latitudes, as well as at the polar region. Severe scintillations can degrade the tracking performance of a receiver in terms of cycle slips and increased navigation error or even cause the receiver to stop tracking. Such transient stop tracking of GNSS signal is due to the carrier phase variation being out of range of a technically set phase-locked loop (PLL), or the received signal amplitude being lower than a preset threshold, or the phase/amplitude variations being too fast to be tracked. 1997; Van Dierendonck et al., 1993). One cannot fully separate the influences of phase and amplitude variations on the tracking performance of ground-based receivers, as the deepest amplitude fades usually occur during the fastest phase variations. However, Sust et al. (2014) found that the GPS receiver on board Swarm showed strong phase scintillation but no discernable fluctuations on the signal amplitude (carrier-to-noise-density ratio, C/N 0 ) when loss-of-lock incidents happened. This is also evidenced in Figure 1 of ; when transient GPS signal losses were observed at all tracking channels of Swarm, almost no fades of C/N 0 were observed. A recent work from Xu et al. (2018) provided simulations of the phase and amplitude scintillations for GPS receivers on board a LEO satellite, by using a two-component power law phase screen model (e.g., Carrano & Rino, 2016). They showed that when a LEO satellite is inside the plasma irregularities, only phase scintillation but no amplitude scintillation can be observed. However, when the phase screen in the model is moved further above the LEO satellite, the amplitude scintillation, S 4 , starts to increase gradually and reaches a saturation value of 0.8 when the phase screen is located at 100-200 km above the LEO satellite.
Until now, the model simulation of Xu et al. (2018) has not been verified by using real GNSS measurements that are located at different distances with respect to the irregularity slab. GNSS receivers on board LEO missions that orbit the Earth at different altitudes provide a good opportunity for such a purpose. In this study, we provide the first comparison of GPS signal amplitude variations from receivers on board LEO satellites at different altitudes: the Swarm satellites at about 450 km, the Challenging Minisatellite Payload (CHAMP) at about 400 km, and the GOCE satellite at about 250 km. In addition, the GPS measurements from a ground-based receiver located in southern China have also been used for comparison. In the section to follow, we first introduce the three LEO missions and their onboard GPS receivers. An example and statistical results of the amplitude variations when the satellites encounter plasma irregularities are given in section 3. Relevant discussions taking into account previous studies are given in section 4. Section 5 provides our main findings.

Data Set
The Swarm mission, comprising three spacecraft, was launched on 22 November 2013 into a near-polar (87.5°inclination) orbit with initial altitude of about 500 km. From January 2014 onward, the three spacecraft were maneuvered apart and achieved their final constellation on 17 April 2014. From then on, the lower pair (Swarm A and C) is flying side by side with a longitudinal separation of about 1.4°, at an altitude of about 470 km. The third spacecraft, Swarm B, orbits the Earth at about 520 km with a higher inclination of 88°. All three Swarm satellites carry dual-frequency GPS receivers of the same type developed by RUAG Space . The GPS receivers are equipped with eight channels for dual-frequency tracking, which means that the Swarm satellites can simultaneously receive signals from at most eight GPS satellites. During the earlier mission period, all three Swarm satellites delivered GPS data with a time resolution of 10 s, but on 15 July 2014 the receiver configuration was changed, and since then all Swarm satellites are delivering 1 Hz GPS measurements. More detailed information about the technical updates of the Swarm receivers was described by van den Ijssel et al. (2016).
The CHAMP satellite was launched on 15 July 2000, into a near-circular polar orbit (87.3°inclination) with an initial altitude of 456 km. The satellite reentered Earth's atmosphere on 19 September 2010. The primary objectives of CHAMP comprise the accurate determination of the Earth's magnetic and gravitational fields, as well as collecting measurements from the ionosphere and upper atmosphere (Reigber et al., 2002). Among a number of highly accurate instruments, a BlackJack GPS receiver designed by the Jet Propulsion Laboratory was equipped for precise orbit determination (POD) of CHAMP. The GPS measurements were delivered with a time resolution of 10 s. At the beginning of the mission, only eight channels were activated for POD, but after a software update on 5 March 2002, the tracking channels for POD have been increased to 10. Detailed information about the CHAMP GPS receiver can be found in Montenbruck and Kroes (2003).
The GOCE satellite was launched on 17 March 2009, into a near-circular dusk-dawn Sun-synchronous orbit (96.7°inclination) with an initial altitude of 283 km. The satellite reentered Earth's atmosphere on 11 November 2013. The core instrument of GOCE was a three-axis gradiometer for determining the Earth's gravitational field (Rummel et al., 2002). In addition, GOCE was equipped with two 12-channel dual frequency Laben Lagrange GPS receivers for POD (Montenbruck et al., 2006). The main receiver was running in nominal operations and delivered 1 Hz GPS measurements, whereas the other one served as a redundant unit . The extremely low altitude, down to 224 km at the end of the mission, makes GOCE unique compared to other LEO missions.
In addition to observations from the above mentioned LEO satellites, GPS measurements from one station located in southern China, at Nanning (geographic latitude and longitude: 22.84°N and 108.23°E, magnetic latitude: 13.08°N) have also been used for comparison. The station is equipped with a NovAtel GSV4004B receiver, which offers 24 channels for tracking dual-frequency GNSS signal and delivers 20 Hz measurements. More detailed information of this station is given in Cheng et al. (2018). Figure 1a presents the trajectories of visible GPS satellites from the Nanning station (marked with a black pentagon), during 11:30-13:30 Coordinated Universal Time (UTC) on 14 March 2015, when prominent ionospheric scintillations were observed. The height of the ionospheric piercing points of the visible GPS satellites with respect to the station is set to 400 km. The pseudorandom noise (PRN) code of each visible GPS satellite is labeled, and the direction of its trajectory is marked with a blue arrow. The color of the trajectory represents the intensity of amplitude scintillation index, S 4 , measured by the ground-based receiver. The S 4 index is calculated at each 1-min interval. Amplitude scintillation with S 4 > 0.3 mainly occurs for the GPS satellites located southward of the station, for example, PRN = 01, 04, 09, 23, but is also visible for PRN = 16 and 19 at geographic latitude higher than 25°. The most severe scintillation (with S 4 > 0.6) during this period is observed for PRN = 16, at regions close to the East China Sea. However, there are also signals from GPS satellites, like PRN = 17,11,27,28,and 30, showing almost no amplitude scintillation. Figure 1b presents the carrier phase and signal amplitude on the L1 frequency (1,575.42 MHz) of GPS satellite PRN = 04 during the considered 2-hr interval. From top to bottom this figure shows the elevation angle, the detrended and high-pass-filtered (cutoff frequency at 0.1 Hz) carrier phase (Δϕ), the detrended signal amplitude (ΔC/N 0 ), the slant total electron content (STEC), and the phase and amplitude scintillation index, σ ϕ and S 4 , respectively. Similar to S 4 , σ ϕ is calculated at each 1-min interval. Both the σ ϕ and S 4 show prominent fluctuations between 12:00 and 12:50 UTC and reach as high as 1.5 and 0.5, respectively. The STEC decreases and shows also fluctuations during this interval. Figure 1c presents more detailed variations of Δϕ and ΔC/N 0 of PRN = 04 during a 1-min interval (12:37:30-12:38:30 UTC). We see clearly that larger degradation of C/N 0 occurs when larger Δϕ is observed. Around 12:37:38 UTC, the degradation of C/N 0 reaches as much as 20 dB Hz. Under such strong scintillation, the signal from PNR = 04 was interrupted five times (indicated by the red arrows) within the 1-min interval.

Examples of GPS Signal Amplitude Degradation Derived From Receivers on Board LEO Satellites at Different Altitudes
Around 12:43 UTC on the same day, Swarm A and C flew over the Nanning station at about 450 km (see their trajectories in Figure 1a, represented by the magenta and black dash-dot lines, respectively). Figure 2a presents the in situ electron density measured by the onboard Langmuir probe, and the number of tracked GPS satellites from Swarm A. The electron density shows a well-formed equatorial ionization anomaly (EIA), with two crests around ±18°magnetic latitude (MLAT) and a trough above the dip equator.
Compared to the small-scale depletions at the EIA northern crest, the depletions at the southern crest are much stronger. As a result, the tracked GPS satellites are reduced from eight to three at the southern crest region. For the POD of Swarm, the number of tracked GPS satellites should not be less than four; therefore, the epochs with tracked GPS satellites less than four are marked with red color. Figure 2b shows the simultaneous observations from Swarm C, which flies 1.4°eastward of Swarm A. Although the background electron density measured by the two satellites is similar, they probe small-scale plasma irregularities of different structures. Overall, Swarm C observes much stronger depletions at the crests and above the dip equator. Such differences observed by the closely flying Swarm satellites are due to the fact that the postsunset equatorial plasma irregularities usually have longitudinal extensions less than 50 km, which has been discussed in detail by Xiong

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For Swarm C, Figures 2c and 2d show the detrended and high-pass-filtered (cutoff frequency at 0.1 Hz) carrier phase (Δϕ) and C/N 0 on the L1 frequency (black), as well as the elevation angle (red) of each visible GPS satellite, respectively. We have applied high-pass filters with different cutoff frequencies to the carrier phase measurements, but as we focused only on their fluctuations, we finally selected the value, 0.1 Hz, that has been conventionally used for the ground-based receivers (e.g., Van Dierendonck et al., 1993). The epochs with dot-dashed lines indicate that the GPS signal is transiently interrupted. Fluctuations of Δϕ are seen from almost all visible PRN at the EIA crest and trough regions, where the plasma depletions are observed. These fluctuations appear for both low-and high-elevation angles. However, no clear fluctuation of C/N 0 is observed for any PRN, which is different from the ground-based receiver ( Figure 1b). Figure 2e shows the detailed variations of Δϕ and C/N 0 for PRN = 03. Strong fluctuations of Δϕ are found after 12:34 UTC.
Here we would like to note that slight C/N 0 degradations with amplitude less than 1 dB Hz are observed when the elevation angle of PRN = 03 is less than 30°, possibly related to the multipath influence under low elevation angle. Similar fluctuations of Δϕ are found for PRN = 04 (Figure 2f), most prominently at the EIA crest regions when the elevation angle is still larger than 45°. The C/N 0 also degrades by about 2 dB Hz (indicated by a red arrow) before the signal interruption occurred at 12:35 UTC. However, the simultaneous C/N 0 degradation of PRN = 04 from the ground-based receiver at Nanning station reaches as high as 15 dB Hz (not shown here). The comparison between Figures 1b and 2f indicates that when the signal from the same GPS satellite (e.g., PRN = 04) is affected by the plasma irregularities, strong phase variations are seen from both ground-based and spaceborne receivers; however, only the ground-based receiver exhibits significant amplitude fades.

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and high-pass-filtered Δϕ, and the C/N 0 on the L1 frequency for tracked GPS satellite PRN = 09. When CHAMP encounters irregularities at both EIA crests, the tracked GPS satellite number reduces to less than four. We have to note that due to the lower time resolution of CHAMP GPS measurements (0.1 Hz), the cutoff frequency of the high-pass filter was set to 0.025 Hz. As a result, the derived Δϕ varies within ±20 rad, but fluctuations are still observable. Similar to the Swarm receiver, no clear amplitude degradation is observed from the C/N 0 of PRN = 09 before the GPS signal is interrupted. The most intense degradation of C/N 0 appears around 04:04 UTC, with an intensity of less than 2 dB Hz (indicated by a red arrow). The different types of GPS receivers on board the CHAMP and Swarm satellites share a common feature when they encounter strong irregularities in their orbit. The onboard GPS receivers show only strong carrier phase fluctuation but almost no amplitude fades. The result also suggests that the strong phase variation, but not the amplitude degradation, causes the GPS receivers on board LEO satellites, like Swarm and CHAMP, to stop tracking GPS satellites when they are located inside the plasma irregularities. This conclusion is consistent with the result of Xiong, Stolle, et al. (2018), who reported that the occurrence of GPS signal loss was reduced after the PLL bandwidth of the Swarm receivers was widened. For moderate scintillation when the carrier phase variation is still within the PLL bandwidth, the receiver can maintain tracking of GPS signals; however, when the phase variation is too large or too fast, the widened PLL bandwidth is helpless.

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C/N 0 on the L1 frequency. The two crests of EIA are clearly visible from the STEC values on this duskside orbit, which shows also fluctuations close to the magnetic equator that should be related to the small-scale postsunset plasma irregularities, and the tracked GPS satellites reduce from 12 to 4. Strong fluctuations of Δϕ are seen at equatorial latitudes, which is similar to the examples as observed by the Swarm and CHAMP satellites. Relatively slight fluctuation of Δϕ is also observed around −28°MLAT, which is possibly caused by the plasma irregularities at middle latitude as the STEC shows also fluctuations at this latitude. Around 06:12 UTC degradation of signal amplitude by as much as 12 dB Hz is observed at latitudes close to the magnetic equator, which is similar to the behavior of the ground-based receiver. Slight fluctuations of C/N 0 are also observed at other latitudes, but they are within 2 dB Hz.
For comparison, Figure 4b provides another orbit of GOCE but on the dawnside. Similar results are shown from GPS satellite PRN = 13. The relatively smooth variation of STEC indicates that there are no plasma irregularities observed. As a result, neither phase fluctuation nor prominent signal amplitude degradation is observed, and the tracked GPS satellite number keeps more than eight during this period. It is worthy to notice that fluctuations of C/N 0 less than 2 dB Hz are also observed, which indicates that such slight fluctuations of the GPS signal amplitude from the GOCE onboard receiver should be not related to the ionospheric plasma irregularities.

Different Characteristics of GPS Signal Amplitude Degradation for Receivers on Board the Swarm and GOCE Satellites
To have a statistical comparison of the GPS signal amplitude degradation from LEO satellites at different latitudes, we focused on the Swarm C and GOCE satellites, as the GPS receivers from both missions deliver 1-Hz measurements. It is also known that the scintillations are more severe at higher solar flux level; therefore, we choose a 2-year period from August 2014 to July 2016 and from November 2011 to October 2013 for Swarm C and GOCE, respectively. We look at events when transient GPS signal interruptions (less than 10 min) occur. For each event, we use the midpoint between start and end of the interruption to represent its location. In addition, we take only the GPS measurements with elevation angle, α, larger than 45°into account, to reduce the influence of multipath.
The events from both satellites are first separately sorted into geographic latitude and longitude bins (5°× 15°), and within each bin the interruption events from all PRN are added up (Figures 5a and 5c). From a global view, GPS signal interruptions from Swarm C are mainly observed at low latitudes between

10.1029/2019SW002398
Space Weather ±5°and ± 20°MLAT (most prominent at longitudes between −135°and 0°E), as well as at the high latitude (most prominent at longitudes close to the magnetic poles). The GOCE result shows a similar global distribution, but the absolute number of GPS signal interruption is almost 10 times larger than that observed by Swarm C. We further look at their magnetic local time distribution, and the result is shown in Figures 5b and 5d. From both satellites, the low-latitude events appear mainly at postsunset hours and are nearly absent during the other local times, indicating the transient GPS signal interruption at low latitude is caused by the postsunset plasma irregularities. Although there are also low-latitude events observed at dawn hours from GOCE, they are much less (by a factor of 5) when compared to the events at the duskside. The high-latitude events generally have a wider local times distribution. The events around noon are located at higher latitudes and are collocated with the cusp region, while the nightside events prefer to appear at lower latitudes, and they should be collocated with the auroral oval. Similar magnetic local time distribution of transient GPS signal interruption from the Swarm satellites as well as their relation with high-latitude plasma irregularities have been investigated in detail by Xiong, Stolle, et al. (2018); therefore, we do not repeat the discussion here. GOCE satellite has only equatorial orbit crossings at dawn and duskside, but as the southern magnetic pole is located further away to the geographic pole when compared to the northern pole, GOCE can cover almost all the local time at southern high latitude. The nightside events at northern high latitude are confined to the dawn and dusk hours, while southern high-latitude events are somehow shifted toward later local times, and such difference should be caused by the orbit coverage of GOCE at high latitudes. Figures 6a and 6d show the global distribution of the median value of C/N 0 from all PRN on the L1 frequency, for Swarm C and GOCE, respectively. Here, we only consider the periods when transient GPS signal interruption do not happen and used only measurements with elevation angle between the GPS satellite and Swarm/GOCE larger than 45°. The averaged C/N 0 shows almost constant value at all latitude and longitudes, with values of 41.6 and 46.0 dB Hz for Swarm C and GOCE, respectively, which can also be taken as background references for the two spaceborne receivers under situations of no ionospheric plasma irregularities. For comparison, Figures 6b and 6e show the global distribution of the median value of C/N 0 when transient GPS signal interruptions happened. For each event, we considered only 30 s before/after the interruption start/end. From the Swarm C observation, no clear pattern of the C/N 0 can be found, but for the observations from GOCE, C/N 0 is found with lower value where more transient GPS signal interruptions happened. When subtracting the background reference, the degradation of signal amplitude, ΔC/N 0 , is shown in Figures 6c and 6f, and we see that on average ΔC/N 0 reaches about 8 dB Hz at equatorial latitudes and regions close to the magnetic poles, but such feature cannot be seen from the observations of Swarm C. The statistical result is consistent with the examples as shown in our Figures 2 and 4. No prominent GPS signal amplitude degradation can be seen at the Swarm altitude, but an average degradation of about 8 dB Hz (or even larger for some cases) can be seen at the GOCE altitude.
One feature we want to point out is that there are also events from Swarm C, although very few, during which the ΔC/N 0 can be occasionally lower than 30 dB Hz (see the randomly distributed bluish bins in Figures 6b  and 6c). We further checked these events and show one example in Figure 7a. Swarm C encounters postsunset plasma irregularities at the low latitudes well reflected in electron density. The GPS signal interruptions at

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all channels happen at the inner edge of EIA crests where plasma irregularities are strongest. Strong phase fluctuations and signal interruption are seen for PRN = 07, and from 17:21 to 17:24 UTC the signal amplitude drops as low as 20 dB Hz. However, this low signal amplitude suddenly drops to a very low level and then keeps almost constant, which is different from the situation as seen from GOCE onboard receiver that gradually decreases with time ( Figure 4a). Furthermore, we check further observation from the sideby-side flying Swarm A, which encounters similar plasma irregularities and GPS signal interruptions. Strong carrier phase fluctuation from the same GPS satellite, PRN = 07, is also observed, but the signal amplitude keeps around 42 dB Hz and shows only fluctuation within 2 dB Hz. This comparison between Swarm A and C indicates that such occasional sudden drop of received signal amplitude to a very low value is possibly related to the hardware setting of Swarm C onboard receiver but not the scintillation effect.

Radio Wave Propagation Through a Random Media and the Phase Screen Approximation
The study of ionospheric scintillation belongs to the problem dealing with the wave propagation through a random medium. Therefore, the scintillation problem can be solved by finding descriptions that map a point in the probability space of fluctuating media onto a point in the probability space of wavefield (e.g., Yeh & Liu, 1982). The starting point for developing the equations that describe radio wave propagation through a random scattering medium are the Maxwell's equations (e.g., Kintner et al., 2007). The result is typically the derivation of the scalar Helmholtz equation, which represents wave propagation in an irregular medium where single, forward scattering is predominant and where the irregularities have scale sizes larger than the wavelength of the radio wave. The scalar Helmholtz wave equation is defined as where A is the complex amplitude of the electric field, ϵ 1 ð→ r Þ is the deviation from free-space permittivity and characterizes the random variations caused by the plasma irregularities located at → r , and k is the wave number of the incident wave.
Unfortunately, the general solution to equation (1) does not seem to be possible, and one has to settle for various approximate solutions for different applications. An approach, known as parabolic equation method

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(PEM), has been developed for the case of normal incidence wave (e.g., Barabenenkov et al., 1971;Yeh & Liu, 1982). The detailed assumptions and mathematical solutions of PEM approach have been well discussed by Yeh and Liu (1982). In the PEM approach one needs to know the plasma irregularity-induced density fluctuations along the propagation path, which in reality is difficult to get. Although an alternative way is to use an ionosphere model for providing the background plasma density and constrained by the in situ measurements from a satellite as irregularity conditions (e.g., Liu et al., 2012), one still cannot precisely model the plasma density fluctuations along the propagation path of a radio wave.
A more practical approach that has been widely used for calculating the scintillation intensity at ground level is the phase screen approximation, which aims to model the primary effect on wave propagation through Fresnel-scale electron density irregularities as a function of the integral of the permittivity fluctuations along the ray path (e.g., Booker et al., 1950;Rino, 1979aRino, , 1979b. In the phase screen model, the plasma irregularity is defined located within an infinitely thin layer. As emerging the irregularity slab, only the phase of incident wave is affected by the random plasma fluctuations. When the wave propagates further downward, the distorted wave front will set up an interference pattern resulting in amplitude fluctuations. The later process is diffraction, and it depends on the random deviations of the curvature of the phase front, which in turn is determined by the size and strength distributions of the plasma irregularities. The phase screen model basically admits analytic representations of the intensity spectral density function and phase structure function (Carrano & Rino, 2016). As given by Yeh and Liu (1982) and Kintner et al. (2007), the spectrum of the radio wave intensity by amplitude is I = A * A: where Φ I is the Fourier transform of the intensity autocorrelation function, q is the horizontal wave number of the phase fluctuations across the screen, Φ ϕ is the power spectrum of the wave phase exciting the screen and for small changes in phase is linearly related to the irregularity density spectrum, and r F ¼ ffiffiffiffiffiffiffi 2λr p is the Fresnel radius, where λ is the incident signal's wavelength and r is the distance from the irregularity slab to the receiver. The term sin 2 q 2 r 2 F 8π is the Fresnel filtering function. To the first order, this function provides an upper limit on the scale size of irregularities. The upper limit of the scale size is the Fresnel radius, r F , occurring when the sin 2 term goes to 1, that the argument is equal to (2n − 1) π/2 radians. We see that for a given incident wave with wavelength of λ, after emerging from the irregularity slab, it needs to propagate through a certain distance to have the diffraction process, which further causes amplitude scintillation.

The GPS Signal Amplitude Fades Observed at Different Altitudes
The GPS signal amplitude fades observed by the spaceborne receivers at different altitudes shown in our study support the assumption of the phase screen model, that the irregularity slab mainly causes the deviation of radio wave phase but not the radio wave amplitude. That is why, as the Swarm and CHAMP fly inside the irregularity slab, almost no signal amplitude fluctuations (less than 2 dB Hz) are observed. When the waves emerge from the slab and continue to propagate to the ground, amplitude fades can reach up to more than 10 dB Hz for receivers at lower altitude (e.g., GOCE) and ground. The signal amplitude degradation exceeding 10 dB Hz observed by the GOCE satellite provides also direct support for the simulation of Xu et al. (2018).
But one difference between the GOCE observations and simulation of Xu et al. (2018) is that the GPS signal amplitude degradation detected by the GOCE onboard receiver shows much smoother variation (see Figure 4a, and we have also found many similar events). One possible reason could be that Xu et al. (2018) used ground-based measurements as model simulation input but not derived directly from a spaceborne receiver. In most cases, the zonal drift velocity of the ionospheric plasma irregularities has a typical value of 100-200 m/s. Considering the irregularities have outer scale sizes of several hundred kilometers, for a ground-based receiver, the received signal within a short time period, for example, within 1 min, should be affected by the same irregularities or at least the irregularities with structures highly correlated. As a result, the time series (within a short period) of a ground-based receiver reflect mainly influences from the same irregularities. However, the LEO satellite moves at a typical speed of about 7.5 km/s, and compared to this velocity the drift of the irregularities itself can be ignored. Within 1 min the LEO satellites can probe 10.1029/2019SW002398 Space Weather the irregularities at a scale of about 450 km; therefore, the structure of irregularities can change dramatically within such a scale size. As a result, the time series of a spaceborne receiver reflect the influences of irregularities with different structures. Furthermore, the GOCE orbit has an inclination of 96.7°, which means it mainly probes the irregularities along the meridional direction, while the ground-based receiver reflects mainly the zonal structure of the irregularities. This could also contribute to the differences between the observed GOCE signal amplitude degradation and the simulation from Xu et al. (2018).

Different Scenarios for the Radio Occultation and Topside Receivers
For better modeling the propagation of radio waves through the extended random media, which allows both phase and amplitude fluctuations to accumulate within the medium, the phase screen model has been updated by the multiple phase method (e.g., Knepp, 1983;Grimault, 1998), which is especially important when modeling the radio occultation (RO) experiments through the ionosphere, as the radio wave propagation path inside the random medium can be very long (Carrano et al., 2011). In fact, the GPS signal amplitude scintillation from spaceborne RO antennas has been reported by earlier literatures (e.g., Ko & Yeh, 2010;Uma et al., 2012;Wu et al., 2005). However, the RO antenna is in a different orientation compared to the antenna on the topside of a satellite. The RO antenna only tracks GPS signals with elevation angles lower than the horizon, and therefore the GPS signal has a very long propagating path through the ionosphere (Kursinski et al., 2000;Ware et al., 1996). Ko and Yeh (2010) found two typical signal-to-noise ratio fluctuations of RO measurements. One is of a very short interval (∼15 s) when the tangent point height of the occultation ray path is located at E region heights (maximum S 4 at ∼111 km), and the other one is of a longer time interval (∼100 s) when the tangent heights of the occultation ray paths are located at the lower F region heights (maximum S 4 at ∼270 km). In both situations the irregularities are assumed to be located at the tangent point height, from where the distance to the RO receiver on board LEO satellites is far enough (>100-200 km) to be affected by the Fresnel diffractive process, which further causes the signal amplitude fades. In the model simulation of Xu et al. (2018), for the scenario of an occultation receiver on board a LEO satellite, both phase and amplitude scintillations were observed, which is similar to the ground-based receiver.

Summary
In this study we provided a detailed analysis of the received GPS signal amplitude performance from receivers on board LEO satellites at different altitudes. The main findings are summarized as follows: 1. When strong ionospheric plasma irregularities are encountered, the GPS receivers on board Swarm and CHAMP (at about 400-450 km) show both clear carrier phase fluctuations, but almost no amplitude fades (less than 2 dB Hz). The result indicates that it is the strong phase variation that causes the Swarm/CHAMP receivers (located inside the slab of irregularities) to stop tracking the GPS satellites when scintillations happen. 2. For the receiver on board the GOCE satellite at about 250 km, being 100-200 km below the plasma irregularities, events with GPS signal amplitude fades exceeding 12 dB are observed in addition to strong phase variations. By further analyzing 2-year GOCE data, the average signal amplitude degradation reaches 8 dB Hz at both equatorial and polar regions, where transient GPS signal interruptions are frequently observed. 3. These results suggest that the distance from the receiver to the plasma irregularity slab is important, which affects the Fresnel diffractive process in the way to cause the GPS signal amplitude fades.