Four X class solar flares originated from active sunspot region 10930 on 5, 6, 13, and 14 December 2006. Wideband noise from associated solar radio bursts (SRB) on 6, 13, and 14 December drastically reduced the carrier-to-noise ratio (C/No) of the Global Positioning System (GPS) signals. Using specialized high-rate GPS receivers from the AFRL-SCINDA global network, we investigate the impacts of these SRBs on the performance of GPS and quantify the Sudden Increases in Total Electron Content (SITEC) caused by the solar flares. The C/No reduction experienced by a GPS receiver during a SRB depends on the solar incidence angle due to the anisotropy of the antenna gain. We derive an expression for the vertical equivalent C/No reduction due to a SRB in order to compare measurements collected at locations where the solar incidence angles differ. During the SRB on 6 December we observed C/No reductions exceeding 25 dB, intermittent loss of lock, and complete loss of GPS positioning information lasting for several minutes. Peak positioning errors in the horizontal and vertical directions reached 20 and 60 m, respectively. While deep C/No reductions were observed during the SRBs on 6, 13, and 14 December, only the 6 December event was strong enough to substantially degrade GPS tracking and positioning accuracy.
 In December 2006, four X class solar flares originated from active sunspot region 10930. Figure 1 shows the solar X-ray flux measured by the GOES Solar X-ray Imager during a 2-week period encompassing these events. These solar flares were accompanied by solar radio bursts (SRB), some of which had a profound impact on the performance of GPS. In the late 1990s, Klobuchar et al.  predicted that solar radio bursts could affect GPS performance if the solar flux is sufficiently large in the L band frequency range and with Right-Hand Circular Polarization (RHCP) (the polarization to which GPS antennas are receptive). Nevertheless, the direct effects of a solar radio burst on the reception of the GPS signals were not observed until recently [Cerruti et al., 2006]. In this case, a reduction in the carrier-to-noise ratio (C/No) of the GPS signals was observed by receivers on the sunlit hemisphere of Earth during the solar radio burst on 7 September 2005. This occurred because the solar radio signal acts as elevated background noise which competes with the broadcast GPS signals. Even still, the modest reductions in the carrier-to-noise ratios that were observed on this day had little impact on GPS availability or positioning accuracy. The solar radio burst that occurred on 6 December 2006 was of a very different nature: not only was the reception of GPS signals affected, but it was affected enough to degrade GPS availability and positioning accuracy for an extended period of time [Cerruti et al., 2008].
 The frequency response of a solar radio burst is associated with the altitude within the solar atmosphere where the explosive release of energy takes place [Warmuth and Mann, 2005]. This relationship is due to the variation of the plasma parameters such as electron density and magnetic field strength, both of which increase as the altitude within the solar atmosphere decreases. Solar radio bursts releasing large levels of microwave radiation are typically associated with solar flares, which involve both the solar corona and chromosphere. A thorough description of the physical mechanisms on the Sun that gave rise to the 6 December 2006 solar radio burst may be found in the work of Gary .
 The AFRL Scintillation Network and Decision Aid (AFRL-SCINDA) is a network of ground-based receivers that monitor transionospheric signals at the VHF and L Band frequencies. It was established by the Air Force Research Laboratory to provide regional specification and short-term forecasts of scintillation caused by electron density irregularities in the equatorial ionosphere [Groves et al., 1997]. The AFRL-SCINDA network currently includes 30 dual-frequency GPS receivers that record the scintillation intensity index (S4), Total Electron Content (TEC), and its rate of change (ROTI), using the full temporal resolution of the receiver hardware (ranging from 10 to 50 Hz depending on the receiver model) [Carrano and Groves, 2006]. Most of the AFRL-SCINDA ground stations are positioned between the ionization crests of the Appleton anomaly, since ionospheric scintillation is generally most intense in this region of the globe.
2. GPS Performance During the Solar Radio Bursts
2.1. The 5 December 2006 Flare and SRB
 The X9.0 solar flare that occurred on 5 December 2006 was the strongest of the four December flares, at least in terms of X-ray power. It was accompanied by a solar radio burst as well, but the solar radio power in the GPS L1/L2 frequency bands with RHCP was not large enough to cause a detectable reduction in the C/No of the GPS signals. The AFRL-SCINDA GPS receiver at Ascension Island (7.98°S, 345.59°E) was collecting raw 50 Hz measurements during this event, and the C/No of the L1 and L2 signals were unaffected by the solar radio noise. The solar incidence (zenith) angle during the event was approximately 33° (at 1045 UT).
 While the C/No of the GPS signals were unaffected by this solar radio burst, the associated solar flare was detectable because of the impulsive ionization caused by the flare's enhanced EUV radiation. Figure 2 shows the differential pseudorange (in meters) and differential carrier phase (in TEC units) measured during the event. The impulsive enhancement in ionization due to the flare is apparent in the differential carrier phase as a Sudden Increase in Total Electron Content (SITEC) starting at about 1027 UT (which is after the start of the X-ray emission at 1018 UT and before the peak X-ray emission at 1035 UT). During this event the TEC increased by approximately 4.3 TECU in 12 min. Note that while both the differential pseudorange and differential carrier phase provide measures of the TEC, the former is not well suited to the detection of small changes in TEC, as it is generally noisier because of its increased sensitivity to multipath. Also note that the differential carrier phase provides a measure of relative (uncalibrated) slant TEC only, as the instrumental biases associated with the receiver and satellites have not been taken into account. We have subtracted the mean value from the differential carrier phase for convenience in plotting the data.
2.2. The 6 December 2006 Flare and SRB
 The X6.5 solar flare that occurred on 6 December 2006 was associated with a solar radio burst that had the largest impact on GPS signal reception, tracking, and positioning accuracy ever recorded. During the event, the Owens Valley Solar Array (OVSA), operated by New Jersey Institute of Technology (NJIT), measured unusually high levels of RHCP power over a wide range of frequencies in the gigahertz range (Figure 3). The peak RHCP power was estimated to exceed 1 million solar flux units (sfu) (1 sfu = 10−22 W m−2 Hz−1) at the L1 frequency [Cerruti et al., 2008].
Figure 4 shows the L1 and L2 C/No reductions due to this solar radio burst as observed from Ancón, Peru (11.77°S, 282.85°E) on 6 December 2006. We calculate the depth of C/No fading by subtracting a linear fit to the raw C/No measurements in dB-Hz units before and after (and hence uninfluenced by) the solar radio bursts. The solar incidence angle at the midpoint of the time period shown (1915 UT) was 34°. The GPS receiver model was an Ashtech Z-XII which recorded the L1 C/No at 20 Hz and the L2 C/No at 2 Hz. A sustained pattern of deep fading occurred on both the L1 and L2 channels, lasting for about an hour. The deepest C/No fades on L1 and L2 reported by the receiver during the event were approximately 25 and 30 dB, respectively, while the longest-duration C/No fades on L1 and L2 lasted approximately 4 min and 10 min, respectively. It should be noted, however, that the C/No reported by a GPS receiver during periods of intermittent code lock may be subject to some uncertainty, and even under nominal operating conditions can vary from manufacturer to manufacturer. During the periods of strongest solar radio burst power, intermittent loss of lock on the L1 and L2 signals from several GPS satellites occurred, reducing the number of satellites available for computing the receiver position.
 Note that the intermittent pattern of L1 C/No fades is nearly identical for all the GPS satellites on which a lock is maintained, regardless of their azimuth or elevation. This indicates a source of radio noise entering at the GPS antenna and mixing with the signals from each of the satellites, as opposed to, for example, ionospheric scintillation due to electron density irregularities along the path of propagation. The latter would have a different signature for each satellite link. The L1 C/No fades match peaks in the solar radio noise as measured by the OVSA telescope and occur on much longer time scales (up to several minutes) compared with the fades typical of ionospheric scintillation (which are typically shorter than a second). As we shall see, the depth of fading depends on both the solar radio burst RHCP power and the local solar incidence angle. These same comments apply to the L2 C/No fades as well, but since this GPS receiver was not keyed to decode the military (encrypted) Y code, the L2 C/No has been measured with less fidelity than the L1 signal. The L2 fades appear smoother than the L1 fades in Figure 4 primarily because the receiver recorded them at a slower rate.
 The reduction in the L1 and L2 C/No during the solar radio burst had an adverse effect on the measurement of the GPS observables, namely the pseudoranges and carrier phases. Figure 5 shows the differential pseudorange (in meters) and differential carrier phase (in TEC units) measured during the event for several GPS satellites. When the C/No fades were deepest (refer to Figure 4), excursions in the measured differential pseudorange occurred, exceeding 10–20 m frequently and occasionally exceeding several kilometers. These excursions do not accurately reflect the true ionospheric delay; differential pseudorange measurements of this magnitude would imply slant TEC values which are too large to be physically plausible. Instead, these excursions represent errors in the receiver's measurement of the L1 and/or L2 pseudoranges which occur when the low C/No levels are insufficient to maintain code lock on the satellites. While this GPS receiver model has internal logic to exclude some false ranging measurements from the calculation of receiver position (as do most other models), some of these ranging errors remain. These ranging errors contribute, along with the increase in dilution of precision (DOP) because of intermittent loss of lock, to increased GPS positioning errors [Carrano et al., 2005].
Figure 5 (right) shows the SITEC event starting at about 1842 UT (after the start of X-ray emission at 1829 UT and before the X-ray peak emission at 1847 UT) caused by the solar flare's emission in the EUV. During this event, the TEC increased by approximately 3.6 TECU in just 3 min. While there was some indication of a modest reduction in C/No simultaneous with the SITEC event, the bulk of the solar radio power started a few moments later and lasted about an hour longer. The deepest C/No fades (refer to Figure 4) were accompanied by repeated cycle slips in the differential carrier phase, which complicates TEC estimation considerably [Carrano and Groves, 2006]. The complete sequence of events was such that the X-rays from the flare were observed first. These were followed shortly after by a sudden increase in ionization (due to enhanced EUV radiation) which was detected in the GPS TEC. Finally, the solar radio burst was detected through the C/No reduction caused by the elevated wideband noise.
 As a consequence of the reduction in the C/No of the satellite signals due to the increased background radio noise, the receiver began to intermittently lose lock on the satellites. This led to a reduction in the number of satellites available for computing the receiver position. When fewer than four satellites are available, a GPS position outage occurs. Since all of the GPS signals are affected simultaneously by the solar radio burst, the chances of a position outage are relatively high, as compared to the case of ionospheric scintillation which often affects only a few satellite links at a time. Figure 6a shows that the number of GPS satellites used by the receiver decreased from eight to nine to fewer than four during the radio burst. Also shown in Figure 6a is the Geometric Dilution of Precision (GDOP), which is an indicator of the receiver accuracy in position and time due to the geometry of the GPS satellites available for use. During the solar radio burst, GDOP increased from 2 to 4 to a maximum of 43 (excluding outage periods during which GDOP is undefined). The longest GPS outage experienced by this receiver was 155 s, while the total duration of all combined outages during the solar radio burst was 313 s. The horizontal and vertical GPS positioning errors measured are shown in Figure 6b. During the solar radio burst, the largest horizontal and vertical errors briefly reached 20 and 60 m, respectively, although they were typically somewhat less (10 m or less in the horizontal and 40 m or less in the vertical).
2.3. The 13 December 2006 Flare and SRB
 The X3.4 solar flare that occurred on 13 December 2006 was also associated with a solar radio burst that caused significant reduction in the C/No of the L1 and L2 signals. Figure 7 shows the measured C/No fades on L1 and L2 measured at Kwajalein Atoll (9.40°N, 167.47°E) during this solar radio burst. The solar incidence angle during the event (at the midpoint of the time interval shown) was 44°. A strong impulse of solar radio power accompanied by significant C/No reduction occurred at approximately 0223 UT, followed by a brief quiet period and then several rapid C/No fades lasting about an hour in total. The fading patterns are nearly identical for all of the GPS satellites regardless of their elevation and azimuth. The deepest C/No fades on L1 and L2 were approximately 19 dB and 20 dB, respectively. The longest fades on L1 and L2 were roughly 6 and 7 min, respectively. Few loss of lock events resulted from these C/No fades, however.
Figure 8 shows the differential pseudorange (in meters) and differential carrier phase (in TEC units) observed at Kwajalein during the 13 December solar radio burst. The fluctuations in the differential pseudorange were on the order of 5–10 m during the deepest fades and represent unphysical errors in the receiver's measurement of the pseudorange. The differential carrier phase exhibits a SITEC event due to the impulsive ionization caused by the solar flare. The SITEC event began at approximately 0223 UT (after the start of X-ray emission at 0214 UT and before the X-ray peak emission at 0240 UT). Subsequently, the TEC increased by approximately 2.2 TEC units in 4 min. Interestingly, in this case the SITEC event due to the solar flare's emission in the EUV occurred nearly simultaneously with the initial C/No reduction caused by the solar radio noise. The carrier-to-noise ratio reductions were not accompanied by excessive cycle slips.
 Since few loss of lock events were observed as a result of this solar radio burst, the number of satellites used in the position solution was primarily dictated by the geometry of the GPS constellation at the time and the configuration of ground-based obstructions at the site. The maximum value reached by GDOP (not shown) during the event was 5.1. Despite the relatively deep C/No fades observed (refer to Figure 7), horizontal and vertical positioning errors did not exceed 2 m and 4 m, respectively. No GPS outages were observed.
2.4. The 14 December 2006 Flare and SRB
 The X1.5 solar flare that occurred on 14 December 2006 was also associated with a solar radio burst that caused a significant reduction in the C/No of the L1 and L2 signals. Figure 9 shows the C/No fades on L1 and L2 measured at Kwajalein during this solar radio burst. The solar incidence angle at the midpoint of the time period shown (2245 UT) was 44°. The structure of these fades is somewhat different from those measured on 6 and 13 December in that during this event, essentially a single fade of extended duration (approximately 25 min) was observed. Another notable difference is that the fades on L1 are actually deeper than they are on L2. As noted by Cerruti et al. , this must have occurred because the level of RHCP solar radio power at the L1 frequency was larger than it was at the L2 frequency at this time. Figure 10 shows the RHCP solar radio power measured by the OVSA telescope at the time, which confirms this hypothesis. The fading patterns are nearly identical for all the GPS satellites regardless of their elevation and azimuth. The deepest C/No fades on L1 and L2 were approximately 14 dB and 10 dB, respectively. The longest C/No fades on L1 and L2 were roughly 25 min each.
Figure 11 shows the differential pseudorange (in meters) and differential carrier phase (in TEC units) observed at Kwajalein during the 14 December 2006 solar radio burst. Fluctuations in the differential pseudorange were only about 3 m during this event, and these were likely dominated by errors due to multipath. The SITEC event began at approximately 2208 UT, quite a long time after the start of X-ray emission at 2107 UT (according to NOAA's Edited Solar Events Lists), and before the X-ray peak emission at 2215 UT. Subsequently, the TEC increased by approximately 1.1 TEC units in 2 min. While there was some indication of a modest reduction in C/No at the time of the STEC event, the bulk of the solar radio power appears to have arrived approximately 35 min later. The C/No fades were not accompanied by excessive cycle slips.
 Since there were few loss of lock events observed as a result of this solar radio burst, the number of satellites used in the position solution was dictated by the geometry of the GPS constellation at the time and the configuration of ground-based obstructions at the site. The maximum value reached by GDOP (not shown) during the event was 2.4. Despite the relatively deep C/No fades observed (refer to Figure 9), horizontal and vertical positioning errors did not exceed 2 m and 4 m, respectively. No GPS outages were observed.
3. Dependence on the Solar Incidence Angle
 During a solar radio burst, both the intensity of the GPS satellite signals and the solar radio noise are modulated by the gain of the antenna before being processed by the receiver. The GPS satellite signals are amplified according to the antenna gain at the elevation angles of the satellites, whereas the solar radio noise is amplified according to the antenna gain at the angle of solar incidence. Therefore, the depth of C/No fades due to the solar radio burst should depend on the local solar incidence angle. We can use this dependence to estimate the depth of fading that would occur at an arbitrary solar incidence angle. As a useful example, we derive an expression for the “vertical equivalent” C/No fading that would occur if the receiver were located at the subsolar point, which facilitates the comparison of C/No measurements collected at different geographic locations.
 A simple model for the gain of the Ashtech choke ring antenna used to collect the data at Ancón and Kwajalein presented in this paper is graphically illustrated in Figure 12. For this antenna, there is a 9 dB difference between the gain at zenith and the gain at 85° zenith angle. Therefore, one may expect the C/No reduction due to a solar radio burst to be 9 dB deeper at a site located at the subsolar point (where the solar incidence angle is zero) as compared to at a site where the solar incidence angle is 85°.
 We wish to develop an expression for the solar radio burst power and vertical equivalent C/No given the measured C/No and the local solar incidence angle. We neglect atmospheric attenuation which is generally less than 1 dB at L band. Let S represent the power of the broadcast GPS carrier signal for a given satellite, PN represent the system noise (thermal plus cosmic background) in the absence of solar radio burst power, and g(γ) be the antenna gain as a function of the zenith angle, γ, expressed in degrees. In the absence of solar radio noise (indicated by the superscript “0”), the carrier-to-noise ratio depends on the satellite elevation as follows:
where ɛ is the satellite elevation in degrees. Now let PSRB represent the RHCP solar radio power at the GPS L1 frequency. We can express the carrier-to-noise ratio during the solar radio burst as a function of satellite elevation and solar incidence angle as follows:
where θ is the solar incidence angle. We solve for the solar radio burst power using equations (1) and (2) to obtain
Note that the satellite elevation cancels in this expression, as expected. The ratio (C/No)/(C/No)0 (which appears in equation (2) in reciprocal form) represents the C/No fade due to the solar radio burst, in linear units. Thus, it should be possible to measure the RHCP power of a solar radio burst using a GPS receiver provided the C/No fades are large enough to detect and if the system noise (PN) can be adequately characterized. In practice, however, PN is likely to be known only approximately.
 At this point, we can determine the vertical equivalent (zenith) C/No due to the solar radio burst that would be observed if the receiver were located at the subsolar point (0° solar incidence). To do this, we evaluate equation (2) at θ = 0° and combine it with equations (1) and (3) to arrive at an expression for the vertical equivalent C/No (indicated by the superscript “Z”) due to the solar radio burst:
Note that the system noise cancels in this expression. We can use equation (4) to compare the C/No fades from stations where the local solar incidence angles differ. For example, Figure 13 shows the pattern of L1 C/No fades due to the solar radio burst on 6 December 2006 as observed from Ancón, Peru (11.77°S, 282.85°E); Antofagasta, Chile (23.68°S, 289.59°E); Sao Luis, Brazil (2.59°S, 315.79°E); and Kwajalein Atoll (9.40°N, 167.47°E) before and after correcting for the local solar incidence angle. The AFRL-SCINDA GPS receivers at Antofagasta and Sao Luis are Ashtech μZ-CGRS models which record the GPS observables at 10 Hz. Note how remarkably similar the C/No fading patterns are even when measured by GPS receivers separated by thousands of miles. This similarity is even more evident when the vertical equivalent C/No fades are compared. The absence of the large fade at 1853 UT from the measurement at Kwajalein can be explained by the fact that the solar incidence angle exceeded 90° at this time, so that the solar radio noise was very likely blocked by a terrestrial object. Similar results were obtained for the L2 carrier signal, shown in Figure 14. The maximum vertical equivalent L1 and L2 C/No fades during this event were approximately 27 dB and 30 dB, respectively.
 We have investigated the effects of the X class solar flares and the associated solar radio bursts that occurred on 5, 6, 13, and 14 December of 2006 on the GPS receivers of the AFRL-SCINDA global network. The solar radio burst associated with the X9.0 solar flare on 5 December did not cause a detectable reduction in the C/No of the GPS signals. The solar radio bursts on 6, 13, and 14 December, on the other hand, radiated enough microwave power and with the proper polarization (RHCP) to cause severe reduction in the C/No of the GPS signals, lasting up to an hour. During these events, nearly identical patterns of intermittent fading were observed along all GPS satellite links from receivers located on the sunlit hemisphere of Earth (even from receivers separated by thousands of miles). The depth of C/No fades were modulated by the local solar incidence angle due to the anisotropy of the antenna gain. The impacts of these C/No fades on GPS performance may have been exacerbated by the response of the automatic gain control (AGC) circuitry of the receiver, which acts to reduce the total signal received (GPS carrier signals plus noise) in the presence of elevated wideband noise.
 Although the 13 and 14 December solar radio bursts resulted in deep reductions in the C/No, their impacts on GPS tracking and positioning accuracy were minimal. The 6 December solar radio burst, by contrast, was particularly intense and caused profound impacts on GPS performance. During this event, GPS receivers experienced difficulty tracking (increased DOP) and incurred large ranging errors associated with the C/No reduction and intermittent loss of code lock. These combined factors led to elevated GPS positioning errors of up to 20 and 60 m in the horizontal and vertical directions, respectively. The total duration of GPS position outage periods exceeded 5 min during this event.
 SITEC events were observed in conjunction with all four solar flares, at rates between 0.4 and 1.2 TECU/min. These rates were likely also related to the solar incidence angle, although we did not account for this effect when measuring the impulsive increase in TEC. In each case, the complete sequence of events was such that the X-rays from the flare occurred first. These were followed by a sudden increase in ionization (due to enhanced EUV radiation) which was detected in the GPS TEC. Finally (or simultaneously) the solar radio burst was detected through the C/No reduction caused by the elevated wideband noise. We do not mean to suggest that this sequence of events is universal, only that this sequence was followed by the solar events of December 2006.
 We have derived an expression for the vertical equivalent C/No reduction due to a solar radio burst (i.e., the reduction that would occur if the receiver were located at the subsolar point) in order to compare measurements collected at locations where the solar incidence angles differ. This expression suggests that during the 6 December event, the maximum vertical equivalent C/No reductions were 27 dB at L1 and 30 dB at L2. It should be noted, however, that the C/No reported by a GPS receiver during periods of intermittent code lock may be subject to some uncertainty, and even under nominal operating conditions can vary from manufacturer to manufacturer.
 It is interesting that these powerful solar radio bursts occurred during solar minimum conditions. If solar radio bursts with significant power in the gigahertz frequency range are more prevalent during solar maximum conditions when the sun is more active, this could suggest that solar radio bursts may adversely impact GPS operations more frequently than previously anticipated.
 The authors would like to thank Dale Gary of New Jersey Institute of Technology who granted us permission to reprint the figures of solar flux measurements from the OVSA telescope and Paul Kintner of Cornell University for many helpful discussions regarding this work. We would also like to acknowledge Christian Alcala who suggested we account for the GPS antenna gain in our analysis. This work was supported by AFRL contracts FA8718-06-C-0022 and FA8718-08-C-0012.