the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Analysis of Systematic Biases in Tropospheric Hydrostatic Delay Models and Construction of Correction Model
Abstract. In the fields of space geodetic techniques, such as Global Navigation Satellite System (GNSS), tropospheric zenith hydrostatic delay (ZHD) is chosen as the a priori value of tropospheric total delay. Therefore, the inaccuracy of ZHD will definitely infect parameters like the wet delay and the horizontal gradient of tropospheric delay, accompanied by an indirect influence on the accuracy of geodetic parameters, if not dealt with well at low elevation angles. In fact, however, the most widely used ZHD model currently seems to contain millimetre-level biases from the precise integral method. We explored the bias of traditional ZHD models and analysed the characteristics in different aspects on a global annual scale. It was found that biases differ significantly with season and geographical location, and the difference between the maximum and minimum values exceed 30 mm, which should be fully considered in the field of high-precision measurement. Then, we constructed a global grid correction model, which is named ZHD_crct, based on the meteorological data of year 2020 from ECMWF (European Centre for Medium-Range Weather Forecasts), and it turned out that the bias of traditional model in the current year could be reduced by ~50 % when the ZHD_crct was added. When we verified the effect of ZHD_crct on the biases in the next year, it worked almost the same as the former year. The mean absolute biases (MABs) of ZHD will be narrowed within ~0.5 mm for most regions, and the STD (standard deviation) will be within ~0.7 mm. This improvement will be helpful for researches on meteorological phenomena as well.
-
Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
-
Preprint
(3125 KB)
-
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(3125 KB) - Metadata XML
- BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-898', Anonymous Referee #1, 23 Dec 2022
-How much is the difference between synoptic observations (like T and P) and surface data of the ECMWF model?
-I am not sure about the way of your selection for the calculation of tradition and reference outputs. Please explain why you did not use other data sources for the traditional model, such as synoptic data.
-Eq. 8: Please add a few sentences about why you have employed the Fourier function here. Is that because of other researches results, e.g. the GPT model? Please add a reference in this case.Citation: https://doi.org/10.5194/egusphere-2022-898-RC1 -
AC1: 'Reply on RC1', Haopeng Fan, 24 Dec 2022
Thanks for your suggetion.
The purpose of this paper is to explore the deviation between the commonly used dry delay model and the integration method, which is supposed to be the most accurate theoretically. This deviation is very easy to be ignored, but it does exist. Then, we found that it showed a certain rule in the global scope and the whole year, which is one of the main tasks of this paper.
As for the usage of synoptic data you suggest, it is also possible. However, if we want to study the relationship between the traditional model and integration method, we need to use the measured synoptic data of vertical profiles correspondingly. At present, such data can only be obtained by means of sounding balloons or radiosonde. Although there are indeed many such stations around the world, it is not enough for us to study the global bias characteristics, including marine regions. Therefore, we chose ECMWF data, which are more abundant.
As for the Eq.8, we used the Fourier function mainly because of the periodical feature of the biases, which was exposed when we chosed 12 sites over different regions and the annual performance in global analysis. Of course, this method is not firstly proposed by us, and some scholars have also used this method in such as GPT models and many related studies, so I really shall add references for annotation. Thank you very much for your reminder again.
Citation: https://doi.org/10.5194/egusphere-2022-898-AC1
-
AC1: 'Reply on RC1', Haopeng Fan, 24 Dec 2022
-
RC2: 'Comment on egusphere-2022-898', Anonymous Referee #2, 30 Dec 2022
Dear Editor,
The papers tried to analyse the traditional (and updated) zenith hydrostatic delay (ZHD) models and show their deficiencies. The authors proposed a trigonometric model to remove available biases in the traditional ZHD model compared to the reference models based on integration. The results reflect reduced biases, and the model works for a future timeline. Applying the proposed correction model can be useful for meteorological studies, mainly those required to process the signals travelling the atmosphere. I recommend accepting a paper after a round of revision. Please find my comments below to the authors.
Best regards,
--------------------------------------------------------------------------------------------------
Dear Authors,
Thanks for submitting your paper. It is useful for different applications to increase the accuracy of traditional ZHD models using your proposed trigonometric function. However, I have the following comments and questions that may help to increase the quality of your paper:
- Line 37: "To some extend..." - I suggest moving this sentence to the end/middle of the paragraph, starting at line 56. It is unclear here why the ZHD is the key to the total delay determination, and you explained it there.
- Line 88: Put a space between "k" and "represent"
- Table 1: Although you cite the climate type in the Note below the table, I don't understand why you put them in the table. If it is important to know the climate type of the Sites, please define them in a short paragraph, probably as a Note under the table.
- Table 1: There is no info for the Climate Type and Climate name for ST07 to ST12. Probably since they are in the middle of the ocean, this information is not available. If yes, please mention it in the text; otherwise, fill in the blanks in the table with the correct info.
- Line 140: Please elaborate on "half annual items in total energy". It is not clear to the reader.
- Line 142: There is a typo: lager -> larger
- Line 208: Please explain in the text why you provided global distributions of √(a21+a22 and √(a23+a24. Is there any correlation between them?
- Line 212: Please replace "." with ":" after the word "conclusions".
- Figure 9: What is the power of 10 in the left figure, Y-axis?
- Figure 9: Are the figures for "Before Corrections" and "After Corrections" overlapped? If yes, please change the style of one of them to show it better.
- Why did you consider only the SAASD for validation? What is the impact of your proposed correction model in SAASZ?
Best regards,
Citation: https://doi.org/10.5194/egusphere-2022-898-RC2 -
AC2: 'Reply on RC2', Haopeng Fan, 31 Dec 2022
Thanks very much for your detailed comments, which helped us a lot.
Comment 1. Line 37: "To some extend..." - I suggest moving this sentence to the end/middle of the paragraph, starting at line 56. It is unclear here why the ZHD is the key to the total delay determination, and you explained it there.
Reply to Commet 1. Thanks for your suggestion. I put an explanation at line 37 to make it more understandable: "Therefore, if the ZHD contains bias, this error will probably be transmitted to the ZWD, which furtherly exert an influence on the total delay and the final solutions."
Comment 2. Line 88: Put a space between "k" and "represent".
Reply to Comment 2. Sorry for my negligence, and we revised it.
Comment 3. Table 1: Although you cite the climate type in the Note below the table, I don't understand why you put them in the table. If it is important to know the climate type of the Sites, please define them in a short paragraph, probably as a Note under the table.
Reply to Comment 3. Thanks for your advice, and we made an explanation why the climate type matters in this study: " Climate type determines the general weather conditions in this area, thus it probably keeps close relation with ZHD. Since this, the climate type of each site is displayed here for further analysis, which complies with Köppen-Geiger climate classification."
Comment 4. Table 1: There is no info for the Climate Type and Climate name for ST07 to ST12. Probably since they are in the middle of the ocean, this information is not available. If yes, please mention it in the text; otherwise, fill in the blanks in the table with the correct info.
Reply to Comment 4. You’re right about it, and oceans indeed don’t own any climate type in Köppen-Geiger’s model. We explained that under the table: "ST07 to ST12 are located in the middle of ocean, which have no type attribution in Köppen-Geiger’s classification, so a “—” was left in the table above."
Comment 5. Line 140: Please elaborate on "half annual items in total energy". It is not clear to the reader.
Reply to Comment 5. Thanks for your reminder, and we changed it to another explanation: "proportion of annual and semi-annual periodic terms in total energy spectrum".
Comment 6. Line 142: There is a typo: lager -> larger.
Reply to Comment 6. Sorry for the silly mistake, and we revised it.
Comment 7. Line 208: Please explain in the text why you provided global distributions of √(a21+a22 and √(a23+a24. Is there any correlation between them?
Reply to Comment 7. Thanks for your suggestion, and we added a description here: "where a0 denotes the averaged ZHD bias over the whole year, √(a21+a22 and √(a23+a24 denote the amplifications of annual and semi-annual periodic terms, respectively".
Comment 8. Line 212: Please replace "." with ":" after the word "conclusions".
Reply to Comment 8. Thanks for your reminder, and we revised it.
Comment 9. Figure 9: What is the power of 10 in the left figure, Y-axis?
Reply to Comment 9. Sorry that I cut too much on the left side, and we revised it. The power of 10 in the left figure is 4.
Comment 10. Figure 9: Are the figures for "Before Corrections" and "After Corrections" overlapped? If yes, please change the style of one of them to show it better.
Reply to Comment 10. You’re right about it. We enlarged the two figures and made the color blocks translucent, so that they can be distinguished better.
Comment 11. Why did you consider only the SAASD for validation? What is the impact of your proposed correction model in SAASZ?
Reply to Comment 11. Thanks for your question. We chose SAASD just for an example since the difference between the two models is not that large. And we added this explanation at Line 146.
Citation: https://doi.org/10.5194/egusphere-2022-898-AC2
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-898', Anonymous Referee #1, 23 Dec 2022
-How much is the difference between synoptic observations (like T and P) and surface data of the ECMWF model?
-I am not sure about the way of your selection for the calculation of tradition and reference outputs. Please explain why you did not use other data sources for the traditional model, such as synoptic data.
-Eq. 8: Please add a few sentences about why you have employed the Fourier function here. Is that because of other researches results, e.g. the GPT model? Please add a reference in this case.Citation: https://doi.org/10.5194/egusphere-2022-898-RC1 -
AC1: 'Reply on RC1', Haopeng Fan, 24 Dec 2022
Thanks for your suggetion.
The purpose of this paper is to explore the deviation between the commonly used dry delay model and the integration method, which is supposed to be the most accurate theoretically. This deviation is very easy to be ignored, but it does exist. Then, we found that it showed a certain rule in the global scope and the whole year, which is one of the main tasks of this paper.
As for the usage of synoptic data you suggest, it is also possible. However, if we want to study the relationship between the traditional model and integration method, we need to use the measured synoptic data of vertical profiles correspondingly. At present, such data can only be obtained by means of sounding balloons or radiosonde. Although there are indeed many such stations around the world, it is not enough for us to study the global bias characteristics, including marine regions. Therefore, we chose ECMWF data, which are more abundant.
As for the Eq.8, we used the Fourier function mainly because of the periodical feature of the biases, which was exposed when we chosed 12 sites over different regions and the annual performance in global analysis. Of course, this method is not firstly proposed by us, and some scholars have also used this method in such as GPT models and many related studies, so I really shall add references for annotation. Thank you very much for your reminder again.
Citation: https://doi.org/10.5194/egusphere-2022-898-AC1
-
AC1: 'Reply on RC1', Haopeng Fan, 24 Dec 2022
-
RC2: 'Comment on egusphere-2022-898', Anonymous Referee #2, 30 Dec 2022
Dear Editor,
The papers tried to analyse the traditional (and updated) zenith hydrostatic delay (ZHD) models and show their deficiencies. The authors proposed a trigonometric model to remove available biases in the traditional ZHD model compared to the reference models based on integration. The results reflect reduced biases, and the model works for a future timeline. Applying the proposed correction model can be useful for meteorological studies, mainly those required to process the signals travelling the atmosphere. I recommend accepting a paper after a round of revision. Please find my comments below to the authors.
Best regards,
--------------------------------------------------------------------------------------------------
Dear Authors,
Thanks for submitting your paper. It is useful for different applications to increase the accuracy of traditional ZHD models using your proposed trigonometric function. However, I have the following comments and questions that may help to increase the quality of your paper:
- Line 37: "To some extend..." - I suggest moving this sentence to the end/middle of the paragraph, starting at line 56. It is unclear here why the ZHD is the key to the total delay determination, and you explained it there.
- Line 88: Put a space between "k" and "represent"
- Table 1: Although you cite the climate type in the Note below the table, I don't understand why you put them in the table. If it is important to know the climate type of the Sites, please define them in a short paragraph, probably as a Note under the table.
- Table 1: There is no info for the Climate Type and Climate name for ST07 to ST12. Probably since they are in the middle of the ocean, this information is not available. If yes, please mention it in the text; otherwise, fill in the blanks in the table with the correct info.
- Line 140: Please elaborate on "half annual items in total energy". It is not clear to the reader.
- Line 142: There is a typo: lager -> larger
- Line 208: Please explain in the text why you provided global distributions of √(a21+a22 and √(a23+a24. Is there any correlation between them?
- Line 212: Please replace "." with ":" after the word "conclusions".
- Figure 9: What is the power of 10 in the left figure, Y-axis?
- Figure 9: Are the figures for "Before Corrections" and "After Corrections" overlapped? If yes, please change the style of one of them to show it better.
- Why did you consider only the SAASD for validation? What is the impact of your proposed correction model in SAASZ?
Best regards,
Citation: https://doi.org/10.5194/egusphere-2022-898-RC2 -
AC2: 'Reply on RC2', Haopeng Fan, 31 Dec 2022
Thanks very much for your detailed comments, which helped us a lot.
Comment 1. Line 37: "To some extend..." - I suggest moving this sentence to the end/middle of the paragraph, starting at line 56. It is unclear here why the ZHD is the key to the total delay determination, and you explained it there.
Reply to Commet 1. Thanks for your suggestion. I put an explanation at line 37 to make it more understandable: "Therefore, if the ZHD contains bias, this error will probably be transmitted to the ZWD, which furtherly exert an influence on the total delay and the final solutions."
Comment 2. Line 88: Put a space between "k" and "represent".
Reply to Comment 2. Sorry for my negligence, and we revised it.
Comment 3. Table 1: Although you cite the climate type in the Note below the table, I don't understand why you put them in the table. If it is important to know the climate type of the Sites, please define them in a short paragraph, probably as a Note under the table.
Reply to Comment 3. Thanks for your advice, and we made an explanation why the climate type matters in this study: " Climate type determines the general weather conditions in this area, thus it probably keeps close relation with ZHD. Since this, the climate type of each site is displayed here for further analysis, which complies with Köppen-Geiger climate classification."
Comment 4. Table 1: There is no info for the Climate Type and Climate name for ST07 to ST12. Probably since they are in the middle of the ocean, this information is not available. If yes, please mention it in the text; otherwise, fill in the blanks in the table with the correct info.
Reply to Comment 4. You’re right about it, and oceans indeed don’t own any climate type in Köppen-Geiger’s model. We explained that under the table: "ST07 to ST12 are located in the middle of ocean, which have no type attribution in Köppen-Geiger’s classification, so a “—” was left in the table above."
Comment 5. Line 140: Please elaborate on "half annual items in total energy". It is not clear to the reader.
Reply to Comment 5. Thanks for your reminder, and we changed it to another explanation: "proportion of annual and semi-annual periodic terms in total energy spectrum".
Comment 6. Line 142: There is a typo: lager -> larger.
Reply to Comment 6. Sorry for the silly mistake, and we revised it.
Comment 7. Line 208: Please explain in the text why you provided global distributions of √(a21+a22 and √(a23+a24. Is there any correlation between them?
Reply to Comment 7. Thanks for your suggestion, and we added a description here: "where a0 denotes the averaged ZHD bias over the whole year, √(a21+a22 and √(a23+a24 denote the amplifications of annual and semi-annual periodic terms, respectively".
Comment 8. Line 212: Please replace "." with ":" after the word "conclusions".
Reply to Comment 8. Thanks for your reminder, and we revised it.
Comment 9. Figure 9: What is the power of 10 in the left figure, Y-axis?
Reply to Comment 9. Sorry that I cut too much on the left side, and we revised it. The power of 10 in the left figure is 4.
Comment 10. Figure 9: Are the figures for "Before Corrections" and "After Corrections" overlapped? If yes, please change the style of one of them to show it better.
Reply to Comment 10. You’re right about it. We enlarged the two figures and made the color blocks translucent, so that they can be distinguished better.
Comment 11. Why did you consider only the SAASD for validation? What is the impact of your proposed correction model in SAASZ?
Reply to Comment 11. Thanks for your question. We chose SAASD just for an example since the difference between the two models is not that large. And we added this explanation at Line 146.
Citation: https://doi.org/10.5194/egusphere-2022-898-AC2
Peer review completion
Post-review adjustments
Journal article(s) based on this preprint
Viewed
HTML | XML | Total | BibTeX | EndNote | |
---|---|---|---|---|---|
298 | 65 | 14 | 377 | 5 | 3 |
- HTML: 298
- PDF: 65
- XML: 14
- Total: 377
- BibTeX: 5
- EndNote: 3
Viewed (geographical distribution)
Country | # | Views | % |
---|
Total: | 0 |
HTML: | 0 |
PDF: | 0 |
XML: | 0 |
- 1
Siran Li
Zhongmiao Sun
Guorui Xiao
Xinxing Li
Xiaogang Liu
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(3125 KB) - Metadata XML