Estimation and evaluation of hourly MetOp satellites GPS DCBs with two different methods

Li, Linlin; Jin, Shuanggen

doi:https://doi.org/10.5194/angeo-2023-17

Preprints

https://doi.org/10.5194/angeo-2023-17

Preprints

12 Jun 2023

| 12 Jun 2023

Status: a revised version of this preprint was accepted for the journal ANGEO and is expected to appear here in due course.

Estimation and evaluation of hourly MetOp satellites GPS DCBs with two different methods

Linlin Li and Shuanggen Jin

Abstract. Differential code bias (DCB) is one of the Global Positioning System (GPS) errors, which affects the calculation of total electron content (TEC) and ionospheric modeling. In the past, DCB was normally estimated as a constant in one day, while DCB of low Earth orbit (LEO) satellite GPS receiver may have large variations within one day due to complex space environments and highly dynamic orbit conditions. In this study, daily and hourly DCBs of Meteorological Operational (MetOp) satellites GPS receivers are calculated and evaluated using spherical harmonic function (SHF) and local spherical symmetry (LSS) assumption. The results demonstrated that both approaches could obtain accurate and consistent DCB values. The estimated daily DCB standard deviation (STD) is within 0.1 ns in accordance with the LSS assumption and is numerically less than the standard deviation of the reference value provided by the COSMIC Data Analysis and Archive Center (CDAAC). The average error's absolute value is within 0.2 ns with respect to the provided DCB reference value. As for the SHF method, the DCB's standard deviation is within 0.1 ns, which is also less than the standard deviation of the CDAAC reference value. The average error of the absolute value is within 0.2 ns. The estimated hourly DCB with LSS assumptions suggested that calculated results of MetOpA, MetOpB, and MetOpC are, respectively, 0.5 ns to 3.1 ns, -1.1 ns to 1.5 ns, and -1.3 ns to 0.7 ns. The root mean square error (RMSE) is less than 1.2 ns, and the STD is under 0.6 ns. According to the SHF method, the results of MetOpA, MetOpB, and MetOpC are 1 ns to 2.7 ns, - 1 ns to 1 ns, and - 1.3 ns to 0.6 ns, respectively. The RMSE is under 1.3 ns and STD is less than 0.5 ns. The STD for solar active days is less than 0.43 ns, 0.49 ns, and 0.44 ns, respectively, with the LSS assumption, and the appropriate fluctuation ranges are 2.0 ns, 2.2 ns, and 2.2 ns. The variation ranges for the SHF method are 1.5 ns, 1.2 ns, and 1.2 ns, respectively, while the STD is under 0.28 ns, 0.35 ns, and 0.29 ns.

Received: 01 Jun 2023 – Discussion started: 12 Jun 2023

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Linlin Li and Shuanggen Jin

Status: closed

RC1:
'Comment on angeo-2023-17', Anonymous Referee #1, 08 Aug 2023

Review on the manuscript "Estimation and evaluation of hourly MetOp satellites GPS DCBs with two different methods" submitted by Li and Jin to Annales Geophysicae.
The authors present an approach to estimate the MetOp GPS POD receiver DCBs, simultaneously with the topside VTEC from the classical geometry-free phase-code leveling and with an specific ionospheric mapping function previously developed by other authors. The work is of interest but it has a major point, the lack of information and discussion on the topside VTEC results. And this is fundamental to check the quality and consistency of the results in the experience of this reviewer.
1) In the abstract, I suggest, within the sentence
"Differential code bias (DCB) is one of Global Positioning System (GPS) errors, which affects the calculation of total electron content (TEC) and ionospheric modeling."
to replace "which affects" by "which can affect" or "which typically affect" because there are approaches to model and compute the TEC without using pseudoranges, not requiring then to take care on DCBs. They are being used for a long time (Hernández-Pajares et al. 1999), and also recently from the GPS POD MetOp measurements only (Hernández-Pajares et al. 2023).
References:
Hernández-Pajares, M., Juan, J. M., & Sanz, J. (1999). New approaches in global ionospheric determination using ground GPS data. Journal of Atmospheric and Solar-Terrestrial Physics, 61(16), 1237-1247.
Hernández-Pajares, M., Olivares-Pulido, G., Hoque, M. M., Prol, F. S., Yuan, L., Notarpietro, R., & Graffigna, V. (2023). Topside Ionospheric Tomography Exclusively Based on LEO POD GPS Carrier Phases: Application to Autonomous LEO DCB Estimation. Remote Sensing, 15(2), 390.
2) The assessment is based on the comparison of the receiver DCBs with the reference value provided by COSMIC Data Analysis and Archive Center (CDAAC) for the MetOp A, B and C. Why are you not comparing as well the transmitter DCBs with plenty of external determinations from ground GPS data? They can be obtained from the MetOp POD GPS data only, as it has been recently done in Hernández-Pajares et al. 2023 (see reference above).
3) In page 2, lines 31-32, the sentence
"The accuracy can be as large..."
should be replaced by
"The errors can be as large..."
or similar.
4) In Equation (9) the magnitude in the DCB is changed, regarding equations (3) and (8), from range (meters) to time delay (s), by means of the explicit light speed term. A different notation between both expressions of DCBs should be used to avoid confusion for the reader between both sets of equations.
5) At the beginning of page 7, it is indicated that
"In fact, it is also possible to estimate the GPS and receiver DCB simultaneously through certain constraints (Liu et al., 2020)."
A comment on the fact that both GPS and MetOp receiver DCBs can be separately estimated from the MetOp POD GPS data only (Hernández-Pajares et al. 2023) is missed in this last paragraph of section 2.5.
6) [Major point] The overall results and corresponding assessment is exclusively based on the receiver DCBs, compared with the reference value provided by COSMIC Data Analysis and Archive Center (CDAAC) for the MetOp A, B and C. The authors don't provide any information on the VTEC results. And this is an important lack in this work, in the experience of this reviewer, because the feasibility of the obtained VTEC (such as no negative values, very small values at local winter high latitude regions, maximum close to the equator) is a crucial information to assess the quality of the studied approach, mapping and DCBs included.

Citation: https://doi.org/10.5194/angeo-2023-17-RC1
- AC3: 'Reply on RC1', Linlin Li, 28 Aug 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-17/angeo-2023-17-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-17-AC3
RC2:
'Comment on angeo-2023-17', Anonymous Referee #1, 08 Aug 2023

Review on the manuscript "Estimation and evaluation of hourly MetOp satellites GPS DCBs with two different methods" submitted by Li and Jin to Annales Geophysicae.
The authors present an approach to estimate the MetOp GPS POD receiver DCBs, simultaneously with the topside VTEC from the classical geometry-free phase-code leveling and with an specific ionospheric mapping function previously developed by other authors. The work is of interest but it has a major point, the lack of information and discussion on the topside VTEC results. And this is fundamental to check the quality and consistency of the results in the experience of this reviewer.
1) In the abstract, I suggest, within the sentence
"Differential code bias (DCB) is one of Global Positioning System (GPS) errors, which affects the calculation of total electron content (TEC) and ionospheric modeling."
to replace "which affects" by "which can affect" or "which typically affect" because there are approaches to model and compute the TEC without using pseudoranges, not requiring then to take care on DCBs. They are being used for a long time (Hernández-Pajares et al. 1999), and also recently from the GPS POD MetOp measurements only (Hernández-Pajares et al. 2023).
References:
Hernández-Pajares, M., Juan, J. M., & Sanz, J. (1999). New approaches in global ionospheric determination using ground GPS data. Journal of Atmospheric and Solar-Terrestrial Physics, 61(16), 1237-1247.
Hernández-Pajares, M., Olivares-Pulido, G., Hoque, M. M., Prol, F. S., Yuan, L., Notarpietro, R., & Graffigna, V. (2023). Topside Ionospheric Tomography Exclusively Based on LEO POD GPS Carrier Phases: Application to Autonomous LEO DCB Estimation. Remote Sensing, 15(2), 390.
2) The assessment is based on the comparison of the receiver DCBs with the reference value provided by COSMIC Data Analysis and Archive Center (CDAAC) for the MetOp A, B and C. Why are you not comparing as well the transmitter DCBs with plenty of external determinations from ground GPS data? They can be obtained from the MetOp POD GPS data only, as it has been recently done in Hernández-Pajares et al. 2023 (see reference above).
3) In page 2, lines 31-32, the sentence
"The accuracy can be as large..."
should be replaced by
"The errors can be as large..."
or similar.
4) In Equation (9) the magnitude in the DCB is changed, regarding equations (3) and (8), from range (meters) to time delay (s), by means of the explicit light speed term. A different notation between both expressions of DCBs should be used to avoid confusion for the reader between both sets of equations.
5) At the beginning of page 7, it is indicated that
"In fact, it is also possible to estimate the GPS and receiver DCB simultaneously through certain constraints (Liu et al., 2020)."
A comment on the fact that both GPS and MetOp receiver DCBs can be separately estimated from the MetOp POD GPS data only (Hernández-Pajares et al. 2023) is missed in this last paragraph of section 2.5.
6) [Major point] The overall results and corresponding assessment is exclusively based on the receiver DCBs, compared with the reference value provided by COSMIC Data Analysis and Archive Center (CDAAC) for the MetOp A, B and C. The authors don't provide any information on the VTEC results. And this is an important lack in this work, in the experience of this reviewer, because the feasibility of the obtained VTEC (such as no negative values, very small values at local winter high latitude regions, maximum close to the equator) is a crucial information to assess the quality of the studied approach, mapping and DCBs included.

Citation: https://doi.org/10.5194/angeo-2023-17-RC2
- AC1: 'Reply on RC2', Linlin Li, 26 Aug 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-17/angeo-2023-17-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-17-AC1
RC3:
'Comment on angeo-2023-17', Anonymous Referee #2, 18 Aug 2023

This study delves into the estimation of Differential Code Bias (DCB) for the MetOP satellite. Both LSS and SHF methods were utilized to estimate the DCB for periods of one day and one hour. Despite the substantial significance of this topic for highly dynamic low Earth orbit (LEO) satellites, the manuscript presents several concerns:
1. The manuscript acknowledges the correlation between ionospheric conditions and DCB estimation; however, it lacks a comprehensive exploration of this relationship within the experimental section and estimation methodology.
2. Enhancements are needed to ensure logical coherence within the introduction section for enhanced clarity and expression.
3. In lines 204-205, it is stated that "DCB is assumed to remain constant within a day, with daily DCB estimation values for different time periods calculated and depicted in Figure 4 and Figure 5." Nonetheless, Figure 4 seems detached from this statement. Considering the context, Figure 4 would be more appropriately situated around line 159. This entails modifying the reference from Figure 3 in line 159 to Figure 4.
4. The manuscript assesses outcomes using reference values from the COSMIC Data Analysis and Archive Center (CDAAC). Nevertheless, line 246 implies that these reference values lack precision, prompting inquiries about the practical implications of the entire analysis process.
5. Insufficient discussion revolves around the relationship between LEO DCB estimation, ionospheric variations, and spatial environmental changes induced by the dynamic nature of LEO satellites.
Further refinement of the manuscript is imperative, particularly in the sections concerning experimental design, results analysis, and discussion. These refinements are essential to address the aforementioned concerns, thereby enhancing the overall logical coherence and credibility of the article.

Citation: https://doi.org/10.5194/angeo-2023-17-RC3
- AC2: 'Reply on RC3', Linlin Li, 26 Aug 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-17/angeo-2023-17-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-17-AC2

Status: closed

RC1:
'Comment on angeo-2023-17', Anonymous Referee #1, 08 Aug 2023

Review on the manuscript "Estimation and evaluation of hourly MetOp satellites GPS DCBs with two different methods" submitted by Li and Jin to Annales Geophysicae.
The authors present an approach to estimate the MetOp GPS POD receiver DCBs, simultaneously with the topside VTEC from the classical geometry-free phase-code leveling and with an specific ionospheric mapping function previously developed by other authors. The work is of interest but it has a major point, the lack of information and discussion on the topside VTEC results. And this is fundamental to check the quality and consistency of the results in the experience of this reviewer.
1) In the abstract, I suggest, within the sentence
"Differential code bias (DCB) is one of Global Positioning System (GPS) errors, which affects the calculation of total electron content (TEC) and ionospheric modeling."
to replace "which affects" by "which can affect" or "which typically affect" because there are approaches to model and compute the TEC without using pseudoranges, not requiring then to take care on DCBs. They are being used for a long time (Hernández-Pajares et al. 1999), and also recently from the GPS POD MetOp measurements only (Hernández-Pajares et al. 2023).
References:
Hernández-Pajares, M., Juan, J. M., & Sanz, J. (1999). New approaches in global ionospheric determination using ground GPS data. Journal of Atmospheric and Solar-Terrestrial Physics, 61(16), 1237-1247.
Hernández-Pajares, M., Olivares-Pulido, G., Hoque, M. M., Prol, F. S., Yuan, L., Notarpietro, R., & Graffigna, V. (2023). Topside Ionospheric Tomography Exclusively Based on LEO POD GPS Carrier Phases: Application to Autonomous LEO DCB Estimation. Remote Sensing, 15(2), 390.
2) The assessment is based on the comparison of the receiver DCBs with the reference value provided by COSMIC Data Analysis and Archive Center (CDAAC) for the MetOp A, B and C. Why are you not comparing as well the transmitter DCBs with plenty of external determinations from ground GPS data? They can be obtained from the MetOp POD GPS data only, as it has been recently done in Hernández-Pajares et al. 2023 (see reference above).
3) In page 2, lines 31-32, the sentence
"The accuracy can be as large..."
should be replaced by
"The errors can be as large..."
or similar.
4) In Equation (9) the magnitude in the DCB is changed, regarding equations (3) and (8), from range (meters) to time delay (s), by means of the explicit light speed term. A different notation between both expressions of DCBs should be used to avoid confusion for the reader between both sets of equations.
5) At the beginning of page 7, it is indicated that
"In fact, it is also possible to estimate the GPS and receiver DCB simultaneously through certain constraints (Liu et al., 2020)."
A comment on the fact that both GPS and MetOp receiver DCBs can be separately estimated from the MetOp POD GPS data only (Hernández-Pajares et al. 2023) is missed in this last paragraph of section 2.5.
6) [Major point] The overall results and corresponding assessment is exclusively based on the receiver DCBs, compared with the reference value provided by COSMIC Data Analysis and Archive Center (CDAAC) for the MetOp A, B and C. The authors don't provide any information on the VTEC results. And this is an important lack in this work, in the experience of this reviewer, because the feasibility of the obtained VTEC (such as no negative values, very small values at local winter high latitude regions, maximum close to the equator) is a crucial information to assess the quality of the studied approach, mapping and DCBs included.

Citation: https://doi.org/10.5194/angeo-2023-17-RC1
- AC3: 'Reply on RC1', Linlin Li, 28 Aug 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-17/angeo-2023-17-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-17-AC3
RC2:
'Comment on angeo-2023-17', Anonymous Referee #1, 08 Aug 2023

Review on the manuscript "Estimation and evaluation of hourly MetOp satellites GPS DCBs with two different methods" submitted by Li and Jin to Annales Geophysicae.
The authors present an approach to estimate the MetOp GPS POD receiver DCBs, simultaneously with the topside VTEC from the classical geometry-free phase-code leveling and with an specific ionospheric mapping function previously developed by other authors. The work is of interest but it has a major point, the lack of information and discussion on the topside VTEC results. And this is fundamental to check the quality and consistency of the results in the experience of this reviewer.
1) In the abstract, I suggest, within the sentence
"Differential code bias (DCB) is one of Global Positioning System (GPS) errors, which affects the calculation of total electron content (TEC) and ionospheric modeling."
to replace "which affects" by "which can affect" or "which typically affect" because there are approaches to model and compute the TEC without using pseudoranges, not requiring then to take care on DCBs. They are being used for a long time (Hernández-Pajares et al. 1999), and also recently from the GPS POD MetOp measurements only (Hernández-Pajares et al. 2023).
References:
Hernández-Pajares, M., Juan, J. M., & Sanz, J. (1999). New approaches in global ionospheric determination using ground GPS data. Journal of Atmospheric and Solar-Terrestrial Physics, 61(16), 1237-1247.
Hernández-Pajares, M., Olivares-Pulido, G., Hoque, M. M., Prol, F. S., Yuan, L., Notarpietro, R., & Graffigna, V. (2023). Topside Ionospheric Tomography Exclusively Based on LEO POD GPS Carrier Phases: Application to Autonomous LEO DCB Estimation. Remote Sensing, 15(2), 390.
2) The assessment is based on the comparison of the receiver DCBs with the reference value provided by COSMIC Data Analysis and Archive Center (CDAAC) for the MetOp A, B and C. Why are you not comparing as well the transmitter DCBs with plenty of external determinations from ground GPS data? They can be obtained from the MetOp POD GPS data only, as it has been recently done in Hernández-Pajares et al. 2023 (see reference above).
3) In page 2, lines 31-32, the sentence
"The accuracy can be as large..."
should be replaced by
"The errors can be as large..."
or similar.
4) In Equation (9) the magnitude in the DCB is changed, regarding equations (3) and (8), from range (meters) to time delay (s), by means of the explicit light speed term. A different notation between both expressions of DCBs should be used to avoid confusion for the reader between both sets of equations.
5) At the beginning of page 7, it is indicated that
"In fact, it is also possible to estimate the GPS and receiver DCB simultaneously through certain constraints (Liu et al., 2020)."
A comment on the fact that both GPS and MetOp receiver DCBs can be separately estimated from the MetOp POD GPS data only (Hernández-Pajares et al. 2023) is missed in this last paragraph of section 2.5.
6) [Major point] The overall results and corresponding assessment is exclusively based on the receiver DCBs, compared with the reference value provided by COSMIC Data Analysis and Archive Center (CDAAC) for the MetOp A, B and C. The authors don't provide any information on the VTEC results. And this is an important lack in this work, in the experience of this reviewer, because the feasibility of the obtained VTEC (such as no negative values, very small values at local winter high latitude regions, maximum close to the equator) is a crucial information to assess the quality of the studied approach, mapping and DCBs included.

Citation: https://doi.org/10.5194/angeo-2023-17-RC2
- AC1: 'Reply on RC2', Linlin Li, 26 Aug 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-17/angeo-2023-17-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-17-AC1
RC3:
'Comment on angeo-2023-17', Anonymous Referee #2, 18 Aug 2023

This study delves into the estimation of Differential Code Bias (DCB) for the MetOP satellite. Both LSS and SHF methods were utilized to estimate the DCB for periods of one day and one hour. Despite the substantial significance of this topic for highly dynamic low Earth orbit (LEO) satellites, the manuscript presents several concerns:
1. The manuscript acknowledges the correlation between ionospheric conditions and DCB estimation; however, it lacks a comprehensive exploration of this relationship within the experimental section and estimation methodology.
2. Enhancements are needed to ensure logical coherence within the introduction section for enhanced clarity and expression.
3. In lines 204-205, it is stated that "DCB is assumed to remain constant within a day, with daily DCB estimation values for different time periods calculated and depicted in Figure 4 and Figure 5." Nonetheless, Figure 4 seems detached from this statement. Considering the context, Figure 4 would be more appropriately situated around line 159. This entails modifying the reference from Figure 3 in line 159 to Figure 4.
4. The manuscript assesses outcomes using reference values from the COSMIC Data Analysis and Archive Center (CDAAC). Nevertheless, line 246 implies that these reference values lack precision, prompting inquiries about the practical implications of the entire analysis process.
5. Insufficient discussion revolves around the relationship between LEO DCB estimation, ionospheric variations, and spatial environmental changes induced by the dynamic nature of LEO satellites.
Further refinement of the manuscript is imperative, particularly in the sections concerning experimental design, results analysis, and discussion. These refinements are essential to address the aforementioned concerns, thereby enhancing the overall logical coherence and credibility of the article.

Citation: https://doi.org/10.5194/angeo-2023-17-RC3
- AC2: 'Reply on RC3', Linlin Li, 26 Aug 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-17/angeo-2023-17-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-17-AC2

Linlin Li and Shuanggen Jin

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Short summary

In this study, the LSS assumption and SHF method are used to calculate the LEO satellite GPS DCBs. The SHF method is more stable and precise than the LSS assumption. The daily DCB estimation is more accurate and stable than the hourly DCB due to the more amount of data. Hourly DCBs have changes in one day, but these can mainly be attributed to random errors because these error time series conform to a normal distribution.


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