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Keywords:

  • total electron content;
  • data assimilation;
  • ionosphere

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Differential Validation
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[1] This paper presents a validation and accuracy assessment of the total electron content (TEC) from US-TEC, a new product presented by the Space Environment Center over the contiguous United States (CONUS). US-TEC is a real-time operational implementation of the MAGIC code and provides TEC maps every 15 min and the line-of-sight electron content between any point within the CONUS and all GPS satellites in view. Validation of TEC is difficult since there are no absolute or true values of TEC. All methods of obtaining TEC, for instance, from GPS, ocean surface monitors (TOPEX), and lightning detectors (FORTE), have challenges that limit their accuracy. GPS data have interfrequency biases; TOPEX also has biases, and data are collected only over the oceans; and FORTE can eliminate biases, but because of the lower operating frequency, the signals suffer greater bending on the rays. Because of the difficulty in obtaining an absolute unbiased TEC measurement, a “differential” accuracy estimate has been performed. The method relies on the fact that uninterrupted GPS data along a particular receiver-satellite link with no cycle slips are very precise. The phase difference (scaled to TEC units) from one epoch to the next can be determined with an accuracy of less than 0.01 TEC units. This fact can be utilized to estimate the uncertainty in the US-TEC vertical and slant path maps. By integrating through US-TEC inversion maps at two different times, the difference in the slant TEC can be compared with the direct phase difference in the original RINEX data file for nine receivers not used in the US-TEC calculations. The results of this study, for the period of April–September 2004, showed an average root mean square error of 2.4 TEC units, which is equivalent to less than 40 cm of signal delay at the GPS L1 frequency. The accuracy estimates from this “differential” method are similar to the results from a companion paper utilizing an “absolute” validation method by comparing with FORTE data.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Differential Validation
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[2] The ionospheric total electron content (TEC) is a measure of the total number of free electrons along a particular line of sight and is expressed as TEC units (1 = 1016 el m−2). The TEC is an appropriate parameter for the study of the ionospheric conditions and is particularly important for the correction of positioning information for single-frequency GPS user, and for resolving integer ambiguities in dual-frequency GPS receivers [Mader, 1990, 1992]. Ionospheric TEC at a given station can change by tens or even hundreds of TEC units during geomagnetic perturbed conditions [Araujo-Pradere et al., 2006; Araujo-Pradere, 2005; Foster, 1993; Mendillo et al., 1970], which introduces tens of meters error in position.

[3] The NOAA-SEC United States-Total Electron Content (US-TEC) product [Fuller-Rowell et al., 2006] evolved through collaboration between the Space Environment Center (SEC), the National Geodetic Survey (NGS), and the University of Colorado's Cooperative Institute for Research in Environmental Sciences. The model is designed to specify TEC over the continental United States (CONUS) in near real time. The product uses a Kalman filter data assimilation technique and is driven by data from ground-based GPS dual frequency receivers. Data from about 60 stations from the National Differential GPS (NDGPS) network, operated by the U.S. Coast Guard, are ingested into the model. The accuracy of the TEC maps is dependent on the number of stations so efforts are also underway to increase the available real-time stations. US-TEC is currently running as an experimental product at SEC, and will be transitioned to full operations in the spring of 2006.

[4] US-TEC is the real-time implementation of MAGIC (described in detail by Spencer et al. [2004]), a Kalman filter data assimilation scheme, which provides a means of optimally updating a solution of a linear least squares problem given time-dependent observations and an a prior model estimate of the solution. The unknowns, which in this case represent the ionospheric electron density field, are stored in the state vector. Associated with this matrix is a covariance matrix, which is updated by the filter each observation.

[5] Central to the US-TEC assimilation method is the use of empirical orthonormal functions (EOF) in the state vector, which are used in place of a height grid to define the vertical electron density profile. This method of mapping the state vector enables a more succinct representation of the electron density field in three dimensions. The mapping is applied to the radial profile using a set of EOFs, obtained from the IRI95 model [Bilitza, 1997]. This mapping method significantly improves the ability of the filter to image variations in the electron density profile. As an added advantage, the reduction in size of the state vector will also increase performance and reduce memory requirements by one or more orders of magnitude.

[6] An example of the mapping functions is shown in Figure 1. The EOF profiles were generated by applying singular value decomposition to a set of model profiles generated by IRI95. The dominant term, EOF1, represents a mean ionospheric profile. The higher-order EOFs, which gradually decrease in significance, allow the profile to depart from the mean. Typically 2 to 3 EOFs are sufficient when using ground-based data alone.

image

Figure 1. Example empirical orthonormal functions (EOFs).

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[7] The US-TEC model uses the GPS receiver independent exchange format (RINEX) files as input [Gurtner and Mader, 1990]. From this file, GPS observables are extracted from pseudoranges derived from code or carrier phase measurements. The dispersion, or time delay between signals at two frequencies, provides a measure of the integral TEC along the entire propagation path. Determining TEC using carrier phase observations is precise (noise reduced) but ambiguous. The initial integer number N of cycles between the satellite and the receiver is unknown, and this phase ambiguity N remains constant as long as no loss of the signal lock occurs. On the other hand, determining TEC from code pseudorange observations is unambiguous but noisy. Utilizing both the very precise but ambiguous carrier phase observations, and the unambiguous but less precise code pseudorange observations, provide the necessary information to generate the TEC maps.

[8] The output of US-TEC has been validated using two approaches. An absolute method is presented in a companion paper by Minter et al. [2007] that utilizes data from the Fast Onboard Recording of Transient Events (FORTE) satellite [Moses and Jacobson, 2002, 2004], and a “differential” accuracy estimate, which is presented here. The two methods give similar results lending credence to the two methods.

2. Differential Validation

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Differential Validation
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[9] Validation of TEC is difficult since there is no absolute or true value of TEC. All methods of obtaining TEC, for instance, from GPS, ocean surface monitors (TOPEX), and electromagnetic pulse detectors (FORTE), have challenges that limit their accuracy. GPS data have inherent interfrequency biases; TOPEX also has biases and data are collected only over the oceans; FORTE can eliminate biases but because of the lower operating frequency the signals suffer greater bending on the rays. Because of the difficulty in obtaining an absolute unbiased TEC measurement, a “differential” accuracy estimate has been performed.

[10] The differential method relies on the fact that uninterrupted GPS data along a particular receiver–satellite link with no cycle slips is very precise. The phase difference (scaled to TEC units) from one epoch to the next can be determined with an accuracy of less than 0.01 TEC units [Komjathy, 1997]. This characteristic of the phase data can be utilized to estimate the uncertainty in the US-TEC vertical and slant path maps. By integrating through US-TEC inversion maps at two different times, the difference in the slant TEC can be compared with the direct phase difference in the original RINEX data file. For short time separations the errors in the US-TEC maps are expected to be correlated so the error in the differences in the TEC along the two paths would not reflect the true uncertainty in the maps. However, as the time separation becomes longer, the expectation is that the errors in the US-TEC maps become decorrelated, so that the uncertainty in the differenced TEC approaches the true uncertainty. If the analysis is performed at gradually increasing time separations of the two rays, one would expect the uncertainty to approach a constant value if the technique is valid.

[11] Figure 2 illustrates the differential validation method. In the top right plot of Figure 2, each curve represents the biased TEC derived from continuous phase measurements. The values are very precise from one epoch to the next but the absolute level is not known. The positions along each phase loop k, 2k, …, nk etc., represent the times at each successive epochs. We first select two raypaths at closely spaced times, say 10 min, and estimate the TEC difference at the two epochs. The measured difference in TEC value is very precise and is used as the validation data for the metric. We then sample the US-TEC maps at those same two times along the same two slant directions. In this case, since the US-TEC maps are 15 min apart, the two paths would either be from the same map or ones separated by only 15 min. There are many combinations of two raypaths separated by 10 min from a given receiver during a day, as illustrated in the top right plot of Figure 2. By selecting all combinations for a particular receiver to all the satellites in view during a day many data points can be extracted. Comparing them all with the equivalent values from the US-TEC enables the root mean square error (RMSE) to be calculated.

image

Figure 2. Example of calculation of RMSE values for two different intervals.

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[12] This same approach is applied to successively longer time separations of rays. For instance, in the bottom right plot of Figure 2, rays separated by a time of 4k, say, 40 min, are illustrated. This information is again used to compare with the US-TEC values to provide a value for the RMSE at this particular time difference. The left plot of Figure 2 shows an example of all the values of RMSE at all time separations. At short time differences, e.g., point A in the left plot of Figure 2, which corresponds to the top right plot, we expect the uncertainty estimate to be small and not to reflect the true error in the maps. As the time differences increase, the curve is expected to flatten out to a constant value, which is expected to reflect the true uncertainty.

[13] The differential accuracy analysis therefore computes the RMSE between the RINEX TEC difference (ΔTECkL) and US-TEC inversion TEC difference (ΔTECkU) for paths between a given receiver and all satellites in view over the whole day. For a particular station, this provides one value of RMSE for each time separation of rays for a given day.

[14] The TEC difference measured from the carrier phase in the RINEX files, corresponding to rays at times nk and mk is given by

  • equation image

such that

  • equation image

where L represents the carrier phase, N is the ambiguity number, and the TEC values are the precise but biased values extracted directly from the phase measurements.

[15] An equivalent value of TEC difference can be extracted from the US-TEC maps:

  • equation image

where U denotes the model values of TEC sampled from the US-TEC maps along the same two raypaths and at the same times as the phase observations.

[16] The RMSE at a given time difference is obtained from

  • equation image

where M is the total number of pairs of raypaths considered.

[17] The essence of the method is to calculate the daily RMSE for a given set of receivers for all satellites in view and all intervals of time difference from 10 to 160 min.

3. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Differential Validation
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[18] An example of the validation results is shown in Figure 3 for the receiver at Yreka, California, on 25 June 2004. The slant path RMSE for this day is shown with a solid line for successively increasing time separations, up to 160 min. At short time separation the RMSE approaches zero since the errors in the US-TEC maps will tend to correlate and therefore cancel, so will not reflecting the true error. As the time separation increases the RMSE gradually increases until it eventually reaches a plateau, or a constant value, in this case at about 2 TEC units. We anticipate the RMSE value of the plateau represents the true error of slant path TEC in the US-TEC maps. The equivalent error for vertical TEC is expected to be about a factor of 1.3 lower, depending on the average elevation angle of all the satellites in view. Also shown in Figure 3 are the values obtained from the International Reference Ionosphere (IRI) [Bilitza, 1997], which gives error values that are consistently greater than US-TEC. Notice that unlike US-TEC the IRI values of RMSE continue to increase beyond 160 min indicating the true uncertainty in IRI has not yet been sampled.

image

Figure 3. Example of differential TEC validation.

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[19] The estimates of accuracy using the differential method have been performed for nine stations spread over the CONUS in a fairly regular grid in latitude and longitude. The validation stations are given in Table 1, which provides the station code, name, and state. These sites were not included in the original assimilation process used to generate the US-TEC maps. For each of these stations the daily averaged RMSE analysis has been performed every fifth day since the beginning of March 2004.

Table 1. Stations Used in the Differential Validation
CodeNameState
PABHFlorida BeachWashington
YBHBYrekaCalifornia
BILLLake SkinnerCalifornia
CLK1Clark 1South Dakota
HBRKHillsboroKansas
ARP3Aransas Pass 3Texas
WES2Haystack Observatory (Westford)Massachusetts
VIMSVirginia Institute of Marine ScienceVirginia
CCV3Cape Canaveral 3Florida

[20] Table 2 shows the RMSE statistics at a time separation of rays of 160 min, for each of the nine validation stations for every fifth day over the 6-month period from April to September 2004. In most cases the values had reached a plateau by a time separation of 160 min. For comparison, the values from the IRI are also shown. Note that in most cases the RMSE for IRI has not reached a plateau, so the values for IRI shown in Table 2 are not expected to reflect the true uncertainty.

Table 2. RMSE of Differential TEC for the Nine Reference Stations
 AprMayJun
510152025305101520253051015202530
IRI
PABH 3.83.42.43.6 2.73.02.76.44.43.1 2.4 3.35.31.8
YBHB 4.13.23.03.7 3.33.22.87.35.34.0 3.5 4.25.12.9
BILL 4.84.93.54.1 6.23.74.39.25.15.1 5.2 5.16.23.2
CLK1 3.24.52.74.4 3.83.83.16.25.53.3 2.3 3.95.32.4
HBRK 4.65.12.94.1 4.14.73.67.84.94.2 3.2 4.45.93.9
ARP3 4.67.83.85.1 5.24.65.47.24.14.9 4.8 4.55.94.2
WES2 3.74.03.74.0 3.14.52.95.83.43.9 2.7 3.04.53.3
VIMS 4.34.62.64.2 4.24.63.16.84.64.2 3.1 3.45.64.4
CCV3 4.5 2.65.0 5.34.24.55.13.84.6 3.8 4.25.56.9
Ave 4.24.73.04.2 4.24.03.66.94.64.1 3.5 4.05.53.7
 
USTEC
PABH 1.71.71.61.9 1.61.81.93.32.01.6 2.4 1.72.11.8
YBHB 2.01.61.82.3 2.12.02.23.42.52.0 3.5 2.52.42.8
BILL 2.42.42.42.5 2.72.73.15.12.83.0 5.2 3.03.53.1
CLK1 1.51.81.51.8 1.51.81.62.31.91.7 2.3 2.02.52.5
HBRK 1.81.71.51.8 2.22.11.62.52.31.6 3.2 1.72.43.8
ARP3 2.43.43.52.5 2.72.83.44.12.73.4 4.8 3.03.74.2
WES2 1.81.51.61.4 1.72.21.82.81.61.6 2.8 2.02.03.3
VIMS 1.71.71.41.6 1.82.11.72.52.01.3 3.1 1.62.14.4
CCV3 2.5 2.62.9 2.92.32.12.72.22.2 3.9 2.42.46.9
Ave 2.02.02.02.1 2.12.22.23.22.22.0 3.5 2.22.63.6
 
USTEC-IRI
PABH −2.1−1.6−0.8−1.7 −1.1−1.2−0.8−3.1−2.4−1.5 0.0 −1.6−3.20.0
YBHB −2.2−1.6−1.2−1.3 −1.2−1.2−0.6−3.9−2.8−2.0 0.0 −1.7−2.6−0.1
BILL −2.4−2.6−1.1−1.6 −3.5−1.1−1.2−4.1−2.3−2.1 0.0 −2.1−2.7−0.1
CLK1 −1.7−2.7−1.2−2.6 −2.3−2.0−1.5−3.9−3.6−1.6 0.0 −1.9−2.80.0
HBRK −2.8−3.4−1.4−2.3 −2.0−2.6−2.0−5.3−2.6−2.6 0.0 −2.6−3.50.0
ARP3 −2.2−4.4−0.4−2.5 −2.4−1.7−2.0−3.1−1.4−1.5 0.0 −1.6−2.20.0
WES2 −1.9−2.6−2.1−2.6 −1.4−2.2−1.1−3.0−1.8−2.3 0.0 −1.1−2.50.0
VIMS −2.6−2.9−1.2−2.7 −2.3−2.6−1.4−4.3−2.6−3.0 0.0 −1.7−3.50.0
CCV3 −2.0  −2.1 −2.4−1.9−2.4−2.4−1.6−2.4 0.1 −1.8−3.10.1
Ave diff −2.2−2.7−1.0−2.2 −2.1−1.8−1.4−3.7−2.3−2.1 0.0 −1.8−2.90.0
Ap index14106412121379138131111163410
Number of stations 585858595659575958585700958580
 
 JulAugSep
510152025305101520253051015202530
IRI
PABH2.64.14.43.26.11.62.62.04.53.94.02.8 4.22.12.03.02.9
YBHB3.44.54.64.07.32.82.93.84.54.53.94.2 4.43.33.04.14.1
BILL5.05.05.45.27.83.34.05.24.54.04.24.6 3.53.89.74.96.4
CLK12.32.45.54.36.92.63.02.94.13.94.24.5 5.04.72.12.53.1
HBRK3.73.66.04.79.53.53.63.15.33.43.23.5 4.74.92.84.03.4
ARP34.95.15.15.38.13.33.64.64.94.13.26.9 4.24.73.75.75.0
WES22.94.04.95.06.73.03.03.45.83.72.94.8 4.84.22.72.32.5
VIMS3.54.95.84.88.64.02.93.56.02.63.34.7 3.15.32.83.62.9
CCV3 5.96.25.17.63.63.23.26.33.4 4.3 3.14.32.84.23.1
Ave3.54.45.34.67.63.13.23.55.13.73.64.5 4.14.23.53.83.7
 
USTEC
PABH1.91.91.81.63.21.11.61.22.02.01.91.8 1.71.31.61.71.7
YBHB2.02.82.32.12.91.71.91.62.52.62.52.3 2.22.11.82.12.5
BILL3.13.53.43.53.72.12.52.43.02.82.32.9 2.72.68.92.73.5
CLK11.61.52.12.53.21.31.61.91.82.12.42.9 2.22.41.21.31.5
HBRK1.91.62.22.63.91.51.71.72.12.12.32.0 2.02.31.31.61.9
ARP33.42.82.83.92.81.92.72.63.03.51.84.7 3.33.32.32.93.3
WES21.71.92.21.82.91.41.61.92.61.31.82.4 2.32.31.51.41.6
VIMS1.91.72.12.04.01.51.81.92.41.62.32.3 2.02.51.71.51.4
CCV3 2.82.43.03.11.62.02.22.82.4 2.4 2.42.62.12.32.3
Ave2.22.32.42.53.31.61.91.92.52.32.22.6 2.32.42.52.02.2
 
USTEC-IRI
PABH−0.8−2.2−2.5−1.5−2.9−0.4−1.1−0.8−2.5−1.9−2.1−1.0 −2.5−0.8−0.4−1.3−1.2
YBHB−1.4−1.7−2.4−1.9−4.4−1.1−1.0−2.2−2.0−1.9−1.3−1.9 −2.1−1.3−1.2−2.0−1.6
BILL−1.9−1.6−2.0−1.7−4.0−1.2−1.5−2.8−1.5−1.2−1.9−1.7 −0.9−1.2−0.8−2.3−3.0
CLK1−0.7−0.9−3.4−1.8−3.7−1.3−1.4−1.0−2.4−1.8−1.8−1.5 −2.8−2.3−0.9−1.2−1.7
HBRK−1.9−2.0−3.8−2.1−5.6−2.0−1.9−1.3−3.2−1.4−0.8−1.5 −2.7−2.6−1.5−2.4−1.5
ARP3−1.5−2.3−2.3−1.5−5.3−1.4−1.0−2.0−1.8−0.6−1.4−2.2 −1.0−1.4−1.4−2.8−1.7
WES2−1.2−2.1−2.7−3.2−3.7−1.6−1.4−1.5−3.2−2.3−1.0−2.3 −2.6−1.9−1.1−0.9−1.0
VIMS−1.6−3.3−3.7−2.8−4.5−2.5−1.1−1.6−3.6−1.1−1.0−2.4 −1.2−2.8−1.1−2.1−1.5
CCV3 −3.0−3.8−2.1−4.5−2.0−1.2−0.9−3.5−1.0 −1.9 −0.7−1.7−0.7−1.8−0.8
Ave diff−1.4−2.1−3.0−2.1−4.3−1.5−1.3−1.6−2.6−1.4−1.4−1.8 −1.8−1.8−1.0−1.9−1.5
Ap index7899122771471473475141354
Number of stations58595958585758575753495835859585757

[21] The bottom three rows of each month display the RMSE difference between US-TEC and IRI (labeled as USTEC-IRI), the daily Ap, and the average number of stations available for the 96 TEC maps for each day. Note that on days when a few stations are available, the US-TEC RMSE is close to IRI, as expected. On typical days when about 60 stations are consistently available, the uncertainty for the slant path TEC is between 2 and 3 TEC units. The average RMSE for all conditions over the 6-month period is 2.4 TEC units, which is equivalent to a signal delay of less than 40 cm at L1 frequencies. The equivalent vertical TEC uncertainty would be just less than 2 TEC units. The results of this study are consistent with those from an absolute validation method. Minter et al. [2007] found an average slant path TEC RMSE of 2.7 units when comparing US-TEC output against FORTE data.

[22] On the storm day of 25 July 2004 the RMSE rises slightly to 3.3 TEC units while the corresponding value for IRI rises up to 7.6, an increase in the RMSE of over 4 units with respect to the US-TEC values. This behavior is expected because of the steeper gradients existing during geomagnetic storms, which cannot be adequately resolved with the less than 60 stations that were available in real time for US-TEC.

[23] Figure 4 shows a specific example of the contrast between quiet and disturbed conditions. Figure 4 shows the comparison of a quiet (Ap = 3, 15 November 2004) and a disturbed (Ap = 181, 10 November 2004) day for the receiver VIMS, at the Virginia Institute of Marine Science. In the center are the two RMSE plots for this receiver, the upper plot corresponding to the disturbed interval and the lower one for the quiet conditions. For disturbed periods it is possible that a time separation of rays of 160 min is not sufficient for the errors to have reached a plateau. In Figure 4 therefore the time separations have been extended out to 320 min, which is about the maximum time a satellite can be in view continuously. On the left side of Figure 4 shows a table with the RMSE at a time difference of rays of 160 min for the quiet (15 November) and disturbed (10 November) days, and on the right side is the equivalent averaged over ray time differences between 200 and 300 min. For the quiet conditions the uncertainty at the longer time difference averaged over all the validation stations increases very slightly from 2.2 to 2.3 TEC units, and for the disturbed case it increase from 2.6 to 2.8 units. For IRI, the equivalent values are significantly larger, increasing from 4.2 to 4.6 for quiet conditions, and from 8.1 to 9.0 for the disturbed case. The new IRI values at the longer time separations now reflect the true uncertainty in IRI, and both are substantially larger than US-TEC values, 2 units larger for the quiet day and 6.1 units for the disturbed day. Evaluating the impact at greater ray time separation serves as an additional check on the method. The values tend to get a little noisier at the longer time separations because of the decreased chances of having a continuous observation for this length of time. For the routine continuous validation therefore, the values at the shorter time difference of 160 min are used.

image

Figure 4. Comparison of the RMSE for US-TEC (solid curves) and IRI (dashed curves) for (top) quiet and (bottom) disturbed conditions, together with the table of values.

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[24] The variation of the RMSE for US-TEC and IRI as a function of Ap is shown in Figure 5. Figure 5 shows all values from May 2004 to March 2005, including both quiet and disturbed conditions, plotted against the geomagnetic index Ap. The vertical axis is the RMSE and the horizontal axis is the Ap index. The US-TEC RMSE values are represented by squares, and the IRI values as diamonds. The uncertainty of US-TEC and IRI both increase with increasing Ap, but IRI increases much more rapidly. The results indicate that although less than 60 stations are used in US-TEC, the model is able to capture much of the TEC structure expected during storms.

image

Figure 5. RMSE for US-TEC and IRI as a function of the geomagnetic activity.

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4. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Differential Validation
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[25] Because of the difficulty of obtaining absolute values of TEC, a differential validation method has been used to validate US-TEC and provide an estimate of the uncertainty in the TEC maps. The algorithm relies on the fact that given continuous GPS data along a particular receiver-satellite link with no cycle slips, estimates of the phase difference (scaled to TEC units) from one epoch to the next can be determined with an accuracy of less than 0.01 TEC units. By integrating through US-TEC inversion maps at two different times, the difference in the slant TEC can be compared with the direct phase difference in the original RINEX data file. At sufficiently long time differences between rays, the RMSE is expected to approach the true uncertainty. The results of this study for the period of April to September 2004 show an average RMSE in the slant path TEC of 2.4 TEC units, which is equivalent to less than 40 cm of signal delay at L1 frequencies. The results are consistent with the results from a companion study utilizing an absolute validation method, which indicated an uncertainty in the maps of 2.7 TEC units, a little over 40 cm of signal delay at L1.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Differential Validation
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information
  • Araujo-Pradere, E. A. (2005), GPS-derived total electron content response for the Bastille Day magnetic storm at a low mid-latitude station, Geof. Int., 44(2), 211218.
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Differential Validation
  5. 3. Results
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information
FilenameFormatSizeDescription
rds5333-sup-0001-t01.txtplain text document0KTab-delimited Table 1.
rds5333-sup-0002-t02.txtplain text document5KTab-delimited Table 2.

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