Extreme ionospheric anomalies occurring during severe ionospheric activity can pose an integrity threat to users of Global Navigation Satellite System (GNSS) Ground Based Augmentation Systems (GBAS). While most very large spatial gradients in slant ionospheric delay were observed on high-elevation satellites, several extreme gradients were also observed on satellites below 15 degrees elevation. This paper details the study of anomalous ionospheric spatial gradients for low-elevation satellites observed from the 20 November 2003 geomagnetic storm in the Conterminous United States (CONUS). As viewed by a cluster of Continuously Operating Reference Stations (CORS) receivers in northern Ohio, SVN 26 came into view around 20:30 Universal Time (UT) on this day, rose to an elevation angle of about 15 degrees, and set around 22:00 UT. A spatial gradient of 360 mm/km was discovered at 21:20 UT between CORS stations GARF and WOOS, when SVN 26 was at 11 degrees elevation. Ionospheric delay measurements are vulnerable to semi-codeless L2 tracking errors and data post-processing errors, especially when satellites are at low elevation. This paper presents a series of methods to validate observed ionospheric anomaly events using station-wide checks, satellite-wide checks, and manual verification with single-frequency measurements. Spatial gradients discovered at other station pairs and another low elevation satellite with a similar azimuth angle, SVN 29, support that the event of SVN 26 is an ionospheric anomaly as opposed to a receiver fault.
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 Ground Based Augmentation Systems (GBAS) provide differential GNSS corrections and integrity information to aviation users within several tens of kilometers of GBAS-equipped airports. The GBAS ground facility is a reference station equipped with typically four GNSS receivers/antennas sited at surveyed locations and a VHF data broadcast transmitter for sending GBAS corrections to users. This configuration is illustrated in Figure 1. GBAS users improve positioning accuracy by applying the corrections (thus eliminating common errors between users and the reference receivers) to their L1 measurements.
 Differential GBAS user errors due to spatial variations in ionospheric delay are almost negligible in nominal conditions considering that a conservative one-sigma bound on zenith ionospheric spatial gradients is 4 mm/km [Lee et al., 2007] and the separation between GBAS reference stations and users is small. For a GBAS user at a 200-foot decision height (6 km from the GBAS ground facility), the residual range error is 0.004 m/km × 20 km (6 km + 14 km due to the memory of code-carrier smoothing filter) = 0.08 m [Pullen et al., 2009]. Under unusual conditions such as local daytime during ionospheric storms, however, extremely large spatial decorrelation can exist in the ionosphere. In this case, the user and the reference station may experience very different ionospheric delays; thus residual ionospheric errors after differential correction could be unacceptably large. The spatial gradient of as large as 360 mm/km could cause the residual range error of 0.36 m/km × 20 km = 7.2 m. The range errors resulting from this large ionospheric spatial gradient could produce vertical position errors for GBAS users of a few tens of meters when combined with the worst-case satellite/airborne geometries and approach timing.
 Previous research has identified severe ionospheric spatial gradients which cannot be bounded by any reasonable sigma value broadcast by a GBAS reference station and would be a potential threat to GBAS users if undetected by the reference station. Spatial gradients as large as 320 mm/km were first discovered from the analysis of Wide Area Augmentation System (WAAS) data during the 6–7 April 2000 geomagnetic storm [Datta-Barua et al., 2002]. These gradients could be hazardous to GBAS users when they coincide with poor satellite geometries and worst-case aircraft flight paths with respect to the ionospheric front speed and the GBAS reference station [Luo et al., 2004].
 To better understand this threat and its impact, an ionospheric anomaly “threat model” for GBAS needed to be generated that allowed us to predict the maximum position errors that GBAS users might suffer. A detailed data analysis method was developed and used to examine past Global Positioning System (GPS) dual-frequency data collected from the network of Continuously Operating Reference Stations (CORS) [Ene et al., 2005]. The threat model derived from this data analysis is used to determine the worst-case position errors in the presence of ionospheric anomalies. These hypothetical errors can be mitigated to acceptable levels by inflating broadcast integrity parameters in near real time [Lee et al., 2006].
 Developing the ionospheric anomaly threat model for GBAS Category (CAT) I precision approaches [RTCA, Inc., 2004] in the Conterminous United States (CONUS) took several years and required several iterations before it converged to a “final” set of parameter values. The upper bound on the maximum spatial gradient of the current threat model for CONUS was derived from the two largest gradients observed during the geomagnetic storm of 20 November 2003: 412 mm/km at high elevation and 360 mm/km at low elevation [Pullen et al., 2009]. The discovery of gradients of this magnitude, especially on low-elevation satellites (below 15 degrees), was a major surprise to the GBAS community because earlier work (prior to 2007) supported that anomalous spatial gradients at low-elevation could not be larger than roughly 100–150 mm/km (much smaller than for high-elevation satellites). The impact of the enlarged threat space on potential user position errors is significant; thus newly discovered large spatial gradients should be (and were) validated thoroughly before those are incorporated into the threat model.
 A number of physics-based models [Crowley et al., 2006; Huba et al., 2000] and data assimilation models (with real-time measurements) [Schunk et al., 2004; Bust et al., 2007] of the electron density have been developed within the scientific community. A hypothesis has been advanced from this research that electron density enhancements were driven by geomagnetic storms in which ionospheric delay increased at higher altitudes within the ionosphere (instead of being concentrated in the region between 250 and 600 km). If this were the case, signals from GPS satellites at low elevations would be likely to “pass under” the bulk of storm-enhanced density and thus be relatively unaffected. However, this hypothesis of the vertical concentration of ionospheric anomalies is far from validated: the required level of understanding of the structure and variability of the ionosphere during stormy periods is lacking at present. Given that theoretical models of ionospheric behavior under storm conditions remain questionable, the role of empirical data analysis and validation becomes more important in constructing an ionospheric anomaly threat model.
 This paper present a methodology for analyzing and validating the extreme ionospheric gradients on low-elevation satellites and investigates the event that produced the largest low-elevation gradient (360 mm/km) seen to date. The validation of ionospheric spatial gradient estimates at low elevation is particularly difficult because of both the lack of concrete physical understanding on ionospheric behavior during geomagnetic storms and the prevalence of low-quality measurements (due to additional noise and more frequent loss-of-lock on L2 tracking loops) at low elevation angles. Section 2 introduces the data used to estimate ionospheric spatial gradients and reviews the data analysis procedures to generate ionospheric anomaly candidates. Section 3 presents the largest ionospheric spatial gradients at low elevation observed in northern Ohio during the 20 November 2003 geomagnetic storm. In section 4, this event is validated manually using single-frequency measurements. Sections 5 and 6 describe station-wide and satellite-wide validation methods and present validation results. Section 7 presents our concluding remarks.
2. Data and Analysis Procedure
 On 20 November 2003, the effects of an earlier coronal mass ejection (CME) from the Sun triggered one of the most severe geomagnetic storms of the past solar cycle. This led to an extremely anomalous pattern of ionospheric delay over the American sector during the local afternoon. This event has been classified as a storm-enhanced density (SED), although its unique nature makes this somewhat uncertain. This “SED-like event” was shown to feed a plasmaspheric plume that appeared as a filament structure over the eastern United States [Foster et al., 2004], as shown in the map of ionospheric delay in Figure 2. Ranging delay errors of the GPS L1 signal in the slant direction (i.e., along the actual path between satellite and receiver) were measured from a network of GPS receivers and converted to equivalent vertical delays (i.e., in the zenith or 90-degree upward direction above the observing receiver) via a geometric mapping function by approximating the ionosphere with a thin-shell model located at 350 km above the surface of the Earth [Lee et al., 2007]. The vertical delays at the ionospheric pierce point (IPP), at which the line of sight between satellite and receiver and the thin-shell ionosphere intersect, are then bi-linearly interpolated between each set of three nearest IPPs to create the contour map. Color contours in Figure 2 correspond to the resulting delays from 0 (blue) to 20 (red) meters. The most significant spatial gradients appeared on the edges of the filament of enhanced delay. Among these observations, the largest gradients seen on low-elevation satellites (under 15 degrees elevation) were examined in detail in this study.
 The data used to estimate ionospheric spatial gradients are precise ionospheric delay measurements generated by the Jet Propulsion Laboratory (JPL) using the “Supertruth” processing algorithm [Komjathy et al., 2004, 2005]. Dual-frequency GPS measurements collected from the CORS and International GNSS Service (IGS) networks were processed using NASA's JPL GPS-inferred positioning system (GIPSY) module Sanity Edit (SanEdit) and the JPL's global ionosphere mapping (GIM) software to detect cycle slips, estimate satellite and receiver interfrequency biases, and provide high-precision dual-frequency ionospheric delay estimates, IDF.
 The overall procedure for estimating ionospheric spatial gradients, identifying ionospheric anomalies, and validating anomalies that are due to ionospheric events was established in prior work [Ene et al., 2005; Pullen et al., 2009] and may be summarized as follows. Using the JPL post-processed “Supertruth” data, slant spatial gradients, ∇I, at time t are computed by dividing the difference in slant ionospheric delay between two stations i and j viewing the same satellite k by the distance, d, between those two stations as measured on the Earth's surface.
 This technique is known as the “station-pair method” [Lee et al., 2007]. Stations and times with apparently severe spatial gradients are output to automated screening algorithms that attempt to remove receiver glitches or post-processing errors from consideration. However, automated algorithms cannot eliminate all anomaly candidates that are caused by faulty measurements and thus are not real. Thus, it is necessary to examine all candidates that survive the automated screening process manually to determine whether they resulted from real ionospheric events.
 Several measurement problems can make large ionospheric spatial gradients appear where none actually exist. Dual-frequency data are prone to semi-codeless tracking errors on L2 measurements, particularly for satellites at low elevation angles which have weaker received signal strengths. Short, disconnected arcs of measurements caused by frequent L2 loss of lock as well as higher noise and multipath errors at low elevation may introduce post-processing errors to ionospheric delay estimates. Therefore, anomalous spatial gradients observed at low elevation have to be validated in multiple ways before they can be declared to be real ionospheric events as opposed to artifacts of erroneous measurements.
 Validation of severe spatial gradients was performed in three steps in this study. The first step is to compare the dual-frequency observation with the observation based on only the L1 frequency code-carrier divergence. The L1-only measurement is more robust to outages and cycle slips. In the second step, the ionospheric delays of the station pair from which an anomaly candidate is observed are compared to those of neighboring stations. The third step is to examine the ionospheric delays of other satellites in a similar azimuthal direction and time window. While all three of these tests may not be conclusive due to limited data from nearby stations or satellites, all of them must be passed to the degree that they are possible for an observation to be validated. More details follow in sections 4, 5, and 6.
3. Extreme Ionospheric Spatial Gradient Observed in CONUS
 In this section, we present the largest spatial gradient at low elevation observed in northern Ohio where the maximum spatial gradient at high elevation was also discovered [Pullen et al., 2009] and validate this event in the following sections. The location of CORS receivers (marked with filled circles) in the Ohio/Michigan region tracking GPS SVN 26 is shown in Figure 3. Arcs indicate the track of the IPPs of SVN 26 from 20:30 to 21:30 UT. Lines point from each of the stations to the theoretical IPP (assumed to be at an altitude of 350 km) at 20:30 UT. Note that the azimuthal direction at which SVN 26 is viewed is similar to the orientation of the red-colored region of enhanced delay shown in Figure 2. For this reason, we expect pairs of stations whose lines of sight straddle the red-colored region to exhibit particularly high gradients.
Figure 4 (top) shows the dual-frequency measurements of slant ionospheric delay at the L1 frequency, in meters, observed from two stations WOOS and GARF (shown in Figure 3) to SVN 26 as a function of time in decimal hours. The station WOOS is just to the southwest of the dotted line marking the approximate location of the trailing edge of the enhanced-delay region at 21:00 UT, and GARF lies 75 km northeast of WOOS. By dividing the difference in the apparent delay by their separation distance, the spatial gradient between these two stations is estimated, as shown in Figure 4 (middle). Note that the slope rises from 0 mm/km to nearly 360 mm/km as the delay at WOOS rises to 45 m during passage through the anomalous region, while the delay at GARF stays in a range of about 12–18 m. The elevation angles of SVN 26 in degrees from WOOS (red) and GARF (green) are shown in Figure 4 (bottom). Since these stations are close together from the viewpoint of a satellite far above Earth's surface, their elevation angles to SVN 26 are almost the same and reach a peak of about 12 degrees.
 Data outages on GARF's dual-frequency measurements, however, are visible in Figure 4 (top), and the resulting discontinuity at 20:52 UT in Figure 4 (middle) calls into question the reliability of the dual-frequency estimates of the ionospheric gradient. For this reason, we attempt to “validate” the presence of an actual ionospheric spatial anomaly within this data using single-frequency (L1-only) measurements, as described in the next section.
4. Manual Validation with Single Frequency Measurements
 The first step in validating extreme gradients is to compare the apparent spatial gradient based on the post-processed dual-frequency measurements, to that derived from L1-only code-minus-carrier (CMC) measurements, for the same stations and satellites. The L1-only relative slant ionospheric delay estimate, ICMC, which is half of the measured code-carrier divergence, is
where ρL1 is the GPS L1 pseudorange measurement, and ϕL1 is the L1 carrier phase measurement. ICMC is not subject to fragile L2 tracking loops, but it contains an integer ambiguity of the L1 carrier-phase measurement and greater noise than the carrier-phase L1/L2 estimate due to the presence of L1 code-phase multipath.
 The L1 code-minus-carrier gradient estimate, ∇ICMC, between two stations i and j viewing the same satellite k is computed using the L1 code-minus-carrier delay estimate, ICMC, and is expressed as
where d is the distance between the two stations. ∇ICMC is also subject to the integer ambiguity of ICMC, and thus is “leveled” to the post-processed L1/L2 estimate, ∇IDF. An offset between the L1-only estimate and the L1/L2 estimate at a time well before or after the anomalous ionosphere passes is subtracted from the continuous arc of the L1-only estimate [Ene et al., 2005]. For low-elevation satellites, the continuous arc may not be long enough to capture slopes at the time of quiet ionosphere. Thus, in this study, we manually level the single-frequency gradient estimate, ∇ICMC, to the mean of the dual-frequency estimate. The leveled L1-only estimate of spatial gradient, ∇IL1, is
 The resulting L1-only estimate is accurate enough to validate the dual-frequency estimate if the underlying spatial gradient is large enough to be severely anomalous. The “validated” measurement, ∇IDF_Validated, which survived from the final manual comparison, forms a lower bound on the true spatial gradient by choosing one with a smaller magnitude between the L1-only estimate and the L1/L2 estimate.
The dual-frequency estimate (blue) from Figure 4 (middle) is plotted again in Figure 5 and compared to the single-frequency estimate (green) of the ionospheric spatial gradient derived using this method. Continuous single-frequency measurements exist except at one epoch at 20:52 UT, at which a visible L1 cycle slip occurred and was manually removed. Except for this epoch, the data outages present between 20:52 and 20:54 UT in the dual-frequency measurements do not exist in the L1-only measurements. The two slope estimates show a very similar trend over time, including the periods when L2 data outages occur. Based on this agreement between the two estimates, we conclude (subject to the remaining validation tests) that a slope of about 360 mm/km between the stations WOOS and GARF occurred due to a severe ionospheric anomaly. To date, this is the highest slant ionospheric spatial gradient we have observed at low elevation angle in CONUS.
5. Station-Wide Validation
 Spatial gradients due to L2 cycle slips can be eliminated by manual validation using L1 code-minus-carrier measurements, as described in section 4. However, this type of analysis performed on a station-pair by station-pair basis cannot identify all receiver-instigated events or false anomalies caused by post-processing errors, such as hardware-bias estimation errors or carrier-measurement leveling errors. Thus, another key to validation is a comparison between simultaneous observations of slant delays from nearby stations. If other stations in close proximity exhibit similar patterns of ionospheric delay to the station pair that shows the most-extreme spatial correlation, the observed event is most likely due to the ionosphere as opposed to a single receiver fault.
 To verify the largest spatial gradient observed between WOOS and GARF, we investigated data from nearby stations GUST, LSBN, and FREO, located in northeastern Ohio. Figure 6 shows the dual-frequency measurements of slant ionospheric delay over time from these stations to SVN 26. The slant delays for the three northeastern-most stations, GARF, GUST, and LSBN, remain in about the 10–20 m range. Figure 7 shows the location of these stations, and a dashed line indicates the position and orientation of the ionospheric anomaly (also shown in Figure 2) at 21:00 UT. In contrast, the two stations WOOS and FREO, just to the southwest of the dashed line in Figure 7, begin at 15 m and rise to over 45 m of slant delay during the same period as the lines of sight from these stations to SVN 26 pass through the region of enhanced ionospheric delay. The similarity of the trend for WOOS and FREO suggests that this high rate of change of ionospheric delay is not due to a single receiver failure. The same argument lends confidence to the measurements of GARF, GUST and LSBN.
 In addition to the largest spatial gradient shown in Figure 5, we have validated ionospheric gradients of 200–300 mm/km from stations in Ohio viewing SVN 26 from 20:40 to 21:30 UT. These observations are summarized on the map in Figure 7 with maximum spatial gradient values in mm/km shown in solid lines connecting the pairs of stations from which the estimates were computed.
Figure 8 (top) shows the dual-frequency measurements of slant ionospheric delay at L1, in meters, observed from stations KNTN and SIDN to SVN 26 as a function of time in decimal hours. KNTN begins with a slant delay of about 28 m and, just after 21:10 UT, appears to rise to nearly 40 m. Meanwhile, SIDN has 40-m delays at 20:40 UT that gradually drop to 24 m by 21:30 UT. By dividing the difference in apparent delay by their separation distance of 59 km, the apparent spatial gradient between the stations is estimated as shown in Figure 8 (middle). Note that this reaches a maximum absolute value of about 350 mm/km. The elevation angles of SVN 26 in degrees from KNTN (red) and SIDN (green) are shown in Figure 8 (bottom). From both stations, these elevation angles reach a peak of about 13 degrees.
 Data outages on dual-frequency measurements are visible in Figure 8 (top); thus manual validation is needed. By manually leveling the L1-only computed slope as a function of time to the dual-frequency slope, as described in section 4, we can confirm a lower-bound slope of 300 mm/km at 20:50 UT, as shown in Figure 9. Manual validation was performed for other station pairs in a similar manner, and the values of the resulting validated spatial gradients are indicated by the numbers in Figure 7. The multiple extreme gradients confirmed among nearby pairs of stations provide further support to the conclusion that these observations are due to an actual ionospheric anomaly.
6. Satellite-Wide Validation
 All spatial gradients estimated so far have been for lines of sight toward SVN 26. During the time in which the anomaly was passing over the Ohio/Michigan region, another satellite in addition to SVN 26 was at low elevation and oriented almost parallel to the edge of the anomaly shown in Figure 2: SVN 29. If the signal from another satellite passes through the same region of storm-enhanced density, it is likely that similarly large spatial gradients would be observed from stations viewing that satellite. Thus, another method of verifying an extreme ionospheric spatial gradient at low elevation is to investigate gradient estimates obtained from other low-elevation satellites. This section provides further support that the SVN 26 event is real by showing that large spatial gradients were observed on low-elevation satellite SVN 29 as well.
 To search for other possible high spatial gradients at low elevation, we examine the elevation angle of visible satellites as a function of time, as shown in Figure 10. Although there are as many as 10–12 satellites visible from the Ohio/Michigan region between 20:00 and 21:00 UT, to identify the highest spatial gradients, we have only plotted those whose azimuth angles are aligned within +/−15 degrees of the orientation of the anomaly in Figure 2. The azimuth angle of the edge of the enhanced-delay region is about 307 degrees; thus Figure 10 shows the elevation of those SVs whose azimuth is between 292 and 322 degrees. Each station in Ohio viewing a given satellite observes it at a slightly different elevation. Thus, when plotted together, individual lines to one satellite merge into a single colored region several degrees thick in Figure 10. Satellites that were examined in prior work [Ene et al., 2005] to reveal high ionospheric spatial gradients at high elevation are SVN 38 (yellow-green) at 19:00–20:00 UT, SVN 44 (light purple) at 20:00–22:00 UT, and SVN 46 (black) from 19:30 to 21:00 UT. The elevation angle of SVN 26 (green), which we have analyzed extensively in this paper, is between 10 and 15 degrees from 20:30 to 21:30 UT. Within this time window, another low elevation satellite, SVN 29 (peach), travels across the region of enhanced ionospheric delay.
Figure 11 shows several CORS stations in Ohio and line segments point from each CORS station to the theoretical 350-km-altitude IPPs of SVN 29 at 20:30 UT. This shows that the azimuthal direction is northwest and is closely aligned with the boundaries of the anomaly region in Figure 2. Arcs indicate the position of the IPPs from 20:30 to 21:30 UT as SVN 29 rises and sets. Again, for this reason, we expect pairs of stations whose lines of sight span the region of enhanced delay (indicated with two dashed lines) to show high gradients.
Figure 12 (top) shows the ionospheric slant delays as a function of UT hour observed from two CORS stations, LSBN (red) and FREO (green), viewing SVN 29. In this case, the dual-frequency data are continuous for the entire period. The trend is very similar for both, but the delays for LSBN are up to approximately 9 m larger than those for FREO, because the IPP of FREO moves slightly faster toward southwest direction and escapes from the enhanced-delay region. This difference in delay results in a spatial gradient over time, shown in Figure 12 (middle), of between 100 and 150 mm/km when divided by the station separation distance of 73 km. The elevation of SVN 29 viewed from these two stations, shown in Figure 12 (bottom), ranges from 10–15 degrees for both LSBN and FREO. These spatial gradients are not as extreme as those viewed from SVN 26. However, these gradients are still far larger than typical, and the fact that severe anomalies were observed at another low-elevation satellite whose lines of sight reside in the same region lend strong credence to the worst-case ionospheric spatial gradient observed on SVN 26.
 In this paper, we have applied a two-phase method of ionospheric spatial gradient analysis and validation to observations made on low-elevation satellites on 20 November 2003. This method consists of automatic processing of dual-frequency GPS carrier phase measurements of ionospheric delay combined with manual verification of anomaly candidates generated by automated procedures to search for a lower bound on anomalous ionospheric gradients. Because the ionospheric delay estimates for low-elevation satellites have a higher chance of being corrupted by receiver faults or post-processing errors, more-careful validation is undertaken compared to those of high-elevation satellites. This paper describes three methods used for validation including manual comparison of the dual-frequency estimates to single-frequency code-carrier divergence estimates, cross-checking observations between nearby station pairs, and analysis of ionospheric delays for other low-elevation satellites located in the same region of space.
 This work lends further and more-comprehensive support to the prior validation of low-elevation ionospheric spatial gradients as high as 360 mm/km at L1. These observations were made with CORS network stations in Ohio during the 20 November 2003 geomagnetic storm while tracking SVN 26. Station redundancy rules out the possibility of faulty receivers and significant errors in receiver bias estimation creating an apparent gradient where none existed. Simultaneous observations on another satellite at a similar elevation, while not as extreme as 360 mm/km, were also anomalously high. Observations of ionospheric delay to higher-elevation satellites conducted in other studies [Pullen et al., 2009] corroborates that this was a period of very high spatial gradients of at least 300 mm/km at all elevations. Therefore, we conclude that the gradients observed here are not due to a single satellite fault, satellite bias removal error, or combinations of these causes.
 While this paper analyzes and validates the most extreme low-elevation ionospheric anomaly event observed in CONUS, ionospheric data should continue to be analyzed in case anomalies which cannot be bounded by the current threat model happen to occur, especially during the upcoming solar maximum. More work is also needed to capture anomalous ionospheric behavior in both equatorial and auroral regions to support worldwide GBAS operations. From this study, we conclude that very high spatial gradients on the order of 300–400 mm/km may occur at both high and low elevation angles. The impact of these gradients on WAAS precision navigation integrity is negligible due to the implementation of the WAAS Extreme Storm Detector [Federal Aviation Administration, 2004]. However, as characterized by Pullen et al. , the impact of these ionospheric spatial gradients on GBAS CAT I precision approach user availability is significant if a proper mitigation scheme is not implemented. We will continue to investigate the possibility of a relationship between the worst-case magnitude of ionospheric spatial gradients and satellite elevation to better understand ionospheric behavior and reduce unnecessary conservatism in the resulting ionospheric threat models.
 The authors would like to thank Ming Luo, Todd Walter, and Juan Blanch at Stanford, Jason Rife at Tufts University, Mats Brenner at Honeywell, and John Warburton, Tom Dehel, Barbara Clark, Hamza Abduselam, and Jason Burns of the Federal Aviation Administration (FAA) for their help and support of this work. We would also like to thank Attila Komjathy of the CalTech/Jet Propulsion Laboratory for processing the dual-frequency CORS/IGS data. This study was funded by the FAA Satellite Navigation Local Area Augmentation System (LAAS) Program Office, and the support of Leo Eldredge and Carlos Rodriguez is greatly appreciated. However, the opinions expressed in this paper are solely those of the authors and do not necessarily represent those of the FAA.