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Cross-Comparison and Methodological Improvement in GPS Tomography

Remote Sens. 2020, 12(1), 30; https://doi.org/10.3390/rs12010030

by Hugues Brenot^1,*

, Witold Rohm², Michal Kačmařík³, Gregor Möller⁴, André Sá⁵, Damian Tondaś², Lukas Rapant⁶, Riccardo Biondi⁷

, Toby Manning⁸ and Cédric Champollion⁹

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Reviewer 3: Anonymous

Reviewer 4: Anonymous

Remote Sens. 2020, 12(1), 30; https://doi.org/10.3390/rs12010030

Submission received: 13 November 2019 / Revised: 9 December 2019 / Accepted: 17 December 2019 / Published: 19 December 2019

(This article belongs to the Special Issue GPS/GNSS for Earth Science and Applications)

Round 1

Reviewer 1 Report

A comprehensive work with concrete examples demonstrating a deep understanding of the phenomenon, with possibilities for practical development and evolution

Author Response

A comprehensive work with concrete examples demonstrating a deep understanding of the phenomenon, with possibilities for practical development and evolution.

The authors thank Reviewer 1 for this report.

Reviewer 2 Report

Review of the paper „Cross-comparison and methodological improvement in GNSS tomography” submitted to Remote Sensing.

The paper describes results from different scientific groups and the activities related to tropospheric tomography based on Global Navigation Satellite System data. The paper is methodologically correct but it requires a substantial revision before it can be published.

Major issues:

The goal of the paper is missing. The content of the paper is written in a very chaotic way. I may assume what is the goal of the paper: the summary of different activities from different groups involved in the COST Action. The goal and the particular aims of the paper have to be clearly indicated.

The paper reads like a collection of different results with only a very weak connection between each other. Most of the results were already presented at different conferences, such as EGU, AGU, COST meetings, etc. or published in different papers. This paper lacks a clear connection between different results. There is a mixture of different methodologies, software packages, approaches, data used without clear navigation between the results.

Please changes the structure of the paper. The structure should start with introduction and motivations, methodology, results, summary and conclusions. Now, methodology is spread over different parts of the paper whereas clear summary and conclusion sections are missing.

Please correct your English. Please do not use brackets. Please avoid front loading. Please use the typical structure of sentences in English: Subject+Verb+Object. Looking at the very first sentence “Using GPS data from the Australian CORS, sensitivity and statistical results of GNSS tomography retrievals (water vapour density and wet refractivity) from 5 models have been tested and verified - considering independent observations from radiosonde and radio occultation profiles. “ – this is a perfect example how NOT to construct sentences in scientific English.

Please put your methodology in one place in the paper. Now, different settings are spread over in the text of the manuscript. A good example of the summary is Figure 5. However, this figure should be a table with a better resolution. Please summarize different approaches also in the form of tables.

The title says that you use GNSS data. However, I could not find any results or comparisons from GLONASS, Galileo, BeiDou, etc. If you use only GPS data, please specify it in the title. If you use GNSS, please provide a comparison of troposphere tomography based on different systems, e.g. between Galileo and GPS.

Please provide more details on the GPS solutions, e.g., relative constraining between epochs, absolute constraining, intervals for the ZTD estimates, intervals for gradient estimation, lengths of the solutions, source of the orbits, zero-difference or double-difference solutions, ionospheric-free combinations or L1&L2/L1&L5 combinations, a priori reference frame, co-estimation of station coordinates in center-of-mass or center-of-figure frames, network constraining: no-net-rotation, no-net-translation, etc. Please unify compare all approaches in one common table.

Appendices provide different approaches to GPS tomography from different groups. Please unify the equations. Now, there is a mixture of bold fonts for matrices and vectors. A different nomenclature is used in papers from the field of physics of the atmosphere, satellite geodesy, and remote sensing of environment. Now, the equations represent all styles of writing of equations instead of being consistent.

The paper is very confusing. The abstract starts with the Australian CORS network, and, out of a sudden, there are results from Belgium. Please, make an introduction and show the motivation why you change the area of interest and time of data processing. Please navigate the reader throughout the manuscript and results!

Some figures are of poor resolution, e.g. Fig 9.

It is very unusual that in the last section, which should include the summary, the authors introduce new results and new figures. Please keep the structure of scientific papers as it should be!

Author Response

The authors thank Reviewer 2 for this report. This helps to improve the quality of this manuscript.

Major issues:

The abstract of the manuscript has been modified. The goal of this study is now clearly indicated.

The manuscript has been totally reshaped. Here is the structure of this manuscript:

Section 1: introduction to GPS tomography technique and presentation of the current remaining two limitations (geometrical distribution and convergence in inversion process). Presentation of the motivation/goal of this study to implement methodological improvement according with respect to these two limitations.

Section 2: presentation of the selected meteorological situation for applying our new methodology

Section 3: description of the GPS data and independent observations considered

Section 4: characterisation of the 5 tomography models of this study

Section 5: presentation of the methodology

Section 6: presentation of the statistical results of improved GPS tomography retrievals

Section 7: presentation of cross-comparison of GPS tomography models with profiles from external observations

Section 8: summary, conclusion and perspective

This is true that some of our results have been presented already at EGU, IAG and COST meeting. However, no one of these results are in a publication accepted by a different journal.

Section 5 is dedicated to the presentation of the methodology, section 6 to the results of improved tomography. Section 7 illustrates cross-comparison and Section 8 presents a summary, conclusion and perspective of future work. This manuscript has been reshaped to clarify the link between the different tests and improvements suggested.

Please changes the structure of the paper. The structure should start with introduction and motivations, methodology, results, summary and conclusions.

This is the case now.

Now, methodology is spread over different parts of the paper whereas clear summary and conclusion sections are missing.

Section 5 is now strictly dedicated to the methodology.

We did our best to improve the English and avoid brackets. We simplify as much as possible the text to avoid complicate and unpleasant construction of sentences.

Please put your methodology in one place in the paper.

Done in section 5.

Now, different settings are spread over in the text of the manuscript. A good example of the summary is Figure 5. However, this figure should be a table with a better resolution. Please summarize different approaches also in the form of tables.

The description and specificity of the 5 tomography models has been unified using the same index and symbol for the same parameter or mathematics structure (see Appendices). Figure 5 has been replaced by a Table (Table 2). References to tables have been updated.

The tittle has been change as we only use GPS tomography. GNSS has been replaced by GPS when only GPS is concerned in the frame of this study.

The new paragraph in section 3.1. was added and reads as follows:

The full details of the processing strategy is available in paper by Rohm et al.[36], the data used in this study was derived with a use of “shortest baselines network solution” with following parameters: precise final IGS orbits in IGS05 reference frame, with L3/L5 strategy, minimum constraints applied on the translation parameters for Helmert transformation based on the IGS fiducial stations, elevation dependent weighting, elevation, ZTDs had relative constraints applied, and are estimated in 30 minutes steps with gradients modelled by tilting every 6 hours, , with a 5°-cutoff angle and GMF mapping function [37] considered for geodetic software analysis and retrievals of tropospheric parameters. Thereby, Zenith Total Delays of the neutral atmosphere (ZTDs) and horizontal delay gradients G ⃗=(G_NS,G_EW) have been retrieved every 30 minutes (pice-wise linear function was evaluated every 30 minutes), covering the period from the 3rd to the 10th of March 2010.

Please unify compare all approaches in one common table.

A new Figure (Figure 15) which contents an histogram summarising all approaches, has been added, with associated text, in section 8 (Summary, conclusions and perspectives).

We thought having bold fonts for the key mathematical structure of tomography technique (i.e. matrix and vectors) will improve the read of the appendices. Now we remove all the bold characters of the text. As mentioned before, the description of the 5 tomography models in the Appendices has been unified using the same index and symbol for the same parameter or mathematics structure.

The structure of the manuscript has been changed. Section 6.1.2 is dedicated to the presentation of the results related the use of pseudo-slant observations. After a presentation of the results using CORS network data with the 5 tomography models, the suggested methodological improvement (use of pseudo-observations) is illustrated with data from the Belgium network.

Some figures are of poor resolution, e.g. Fig 9.

The resolution of this Figure has been improved

It is very unusual that in the last section, which should include the summary, the authors introduce new results and new figures. Please keep the structure of scientific papers as it should be!

The content of the last section has been modified. Now a clear summary is presented, with conclusions and perspectives of future work. The figures has been moved in section 6.1.2 (old Figure 17) or removed (Figures 15 and 16; text related to these figure is also removed).

Thank you for your review we find very useful. We think the manuscript is really improved now, and hopefully this answers to your review.

Reviewer 3 Report

The manuscript shows cross-comparison and methodological improvement in GNSS tomography. I have the following comments and questions:

Abstract, line 34: “Finally, a comparison of multi-model tomography with numerical weather prediction shows the relevant use of tomography retrievals to improve the understanding of such severe weather conditions, especially about the initiation of the deep convection.“ Do you refer here to the results shown in section 6? In this section you show the result of a single model (BIRA). i do not see the multi-model result. You show a case study. The wv field from the weather model and tomography are different for this single epoch (figure 15 & 16). How do you know which wv field is correct? I suggest to reformulate your statement somewhat.

Figure 2 and discussion: “(the black circles are the locations of GPS stations and the grey arrows show the horizontal IWV gradients).“ I can hardly see the grey errors. Please increase their size. How did you calculate the iwv gradients?

Line 190: “Note that one-way residual has not been considered in Lazwet and SWD retrievals.“ Why not? Provide recent references to explain this choice. Gradients are taken into account. Why? Provide recent references to explain this choice.

Line 210: according to eq.6 the k factor is the ratio between the SIWV and the SWD You take the k factor from the weather model. This means that you assume that the ratio between the SIWV and the SWD from the weather model is correct. What about severe weather conditions? Comment on this.

Section “2.3.2. Profiles from radio-occultation technique“. I would be cautious with ro refractivity (specific humidity) retrievals below 5 km. For example, a negative bias (preliminary caused by critical refraction) exists around 1 km. Comment on this.

Line 298: “Note that the same apriori condition m0 has been considered by these models. It is based on 6 hours NWP outputs from ACCESS-A, interpolated to the tomography grid of Figure 3. See Puri et al. [32] for more details about the observations assimilated in ACCESS-A using a four-dimensional observation variational assimilation method (4DVAR). In 2010, the radio occultation observations were not assimilated in ACCESS-A system“. What you show in the appendix looks like 3DVAR. Why do you not simply assimilate the SWDs into the weather model? Comment on this.

Section “4.3.2. Interest of pseudo-slant observations for low- and mid-troposphere retrievals“. I do not know what “pseudo-slants“ are. You provide a reference [58] but please provide the formulas too (in the appendix).

Figure 12 and discussion: according to this figure there is some problem with tomography (BIRA, WUELS & UBI) at altitudes > 2 km. You have chosen ACCESS-A as aprior in your tomography. Do you take into account the error statistics of ACCESS-A in your tomography? According to the right hand side of the figure the ACCESS-A errors is about 1 g/kg for altitudes >=2km and about 2 g/kg for altitudes < 2km. I mean if you take into account the error statistics from ACCESS-A in your tomography you should not deviate too much from the ACCESS-A at high altitudes.

Figure 13: in the figure caption you should add ERA(gray). BIRA is blue and not green. The x axis should start at 0. why is there no refractivity > 6km? ro refractivity looks different from all other solutions below 4 km. Is it possible that ro is affected by critical refraction (dN/dz < −157 N‐units per km) in this example?

I suggest to remove line 771 to 787 and Figure 17. The reason is that you refer here to a completely different set up (different location and time, different GPS data processing, different horizontal resolution, one tomography model, etc.).

Author Response

The manuscript shows cross-comparison and methodological improvement in GNSS tomography. I have the following comments and questions:

Line 34 of this abstract has been changed to: “Finally, a comparison of multi-model tomography with numerical weather prediction shows the relevant use of tomography retrievals to improve the understanding of such severe weather conditions.”

Figures 15 and 16 and the related text have been removed from the last section, which is now strictly dedicated to summary, conclusions and perspectives.

OK thanks, the size has been increased.

How did you calculate the iwv gradients?

IWV gradients are estimated from wet gradients, using conversion factor. This explanation has been added in section 2, l.141-142.

The contribution of one-way post-fit residuals to SWDs and SIWVs is still a challenging question and a work in progress (especially to be in nowcasting applications; see Kačmařík et al., 2017).

Kačmařík, M., Douša, J., Dick, G., Zus, F., Brenot, H., Möller, G., Pottiaux, E., Kapłon, J., Hordyniec, P., Václavovic, P., and Morel, L.: Inter-technique validation of tropospheric slant total delays, Atmos. Meas. Tech., 10, 2183–2208, https://doi.org/10.5194/amt-10-2183-2017, 2017.

The following text is mentioned in the last paragraph of this manuscript:

“The hypothesis of straight ray propagating has been considered in this study for modelling path delay from GPS station to ground-based receiver in our tomography models. Because the bending effect is negligible over 10° (Elgered et al., 1991), the inversion problem becomes linear and can be formulated using the discrete theory. However, the bending effect which can affect elevation under 10° (Zus et al., 2012, Möller and Landskron, 2018) has not been considered in our study. Note also that post-fit residuals cleaned from systematic effects, which were not used in this study, could be beneficial for GPS slant observations under severe weather conditions. These two aspects need to be considered in future work.”

The use of NWP to estimate the conversion factor κ is well recognised in GNSS meteorology. However, this is clear that severe weather condition degrades this assumption. This problem is mentioned in the manuscript: “Note this parameter can obtain higher relative error in case of severe weather condition and the occurrence of hydrometeors in the path travel of GNSS signal (Brenot et al., 2006)”; l.406-408 of the new manuscript…. and “Thereby, the contribution of hydrometeors to delay has not been considered. Errors in ground pressure and hydrometeor contributions can impact ZTDs measurements up to few centimetres in extreme weather (Brenot et al., 2006), which can conduct to an error in IWV up to more than 5 kg/m².”; l.808-811 of the new manuscript.

Section “2.3.2. Profiles from radio-occultation technique“. I would be cautious with ro refractivity (specific humidity) retrievals below 5 km. For example, a negative bias (preliminary caused by critical refraction) exists around 1 km. Comment on this.

Critical refraction in the lower troposphere is caused by large vertical gradients in the water vapour fields. The humidity values at high latitudes (>45° and <-45°) (Beyerle et al. 2006) and at altitudes higher than 3 km are in principle too low to produce critical refraction (Gorbunov et al 1996). This profile is between -37° and -39°, the altitudes higher than 2 km and the area of interest has the lowest probability of critical refractivity occurrence according to Beyerle et al. 2006, thus the probability of critical refraction in this example is extremely low even if theoretically possible.

Beyerle et al. https://doi.org/10.1029/2005JD006673

Gorbunov et al. http://hdl.handle.net/21.11116/0000-0003-2D95-3

We agree that the tomography mixed problem as stated in equation (13) is optimal solution for minimisation problem between background and the observations. However, this is one of the minimisation techniques used in the models, and not necessary most successful. We might also say that the models we are developing to be made useful for NWP assimilation would need to be converted to forward, linear and adjoint operator in specific model, which is not a trivial task, definitively beyond scope of this manuscript.

Moreover, this study does not aim for direct improve of NWP initial conditions with GNSS observations, we are rather looking into active weather using tomography retrievals.

Section 5.1.2 of the new manuscript is dedicated to the use of pseudo-slants. The following text provides explanations (l.353-364 of the new manuscript):

“This section presents a methodology based on adding pseudo-slants observations to the systems of equations to be solved. The pseudo-slants have been implemented according to the orientation of delay gradient [57]. To obtain homogeneous repartition of sites (based on CORS network), a distance of 20 km on both side of a station has been considered, in the direction defined by GPS gradient. This means that for 2 pseudo-sites, the wet delay and the water vapour content have been propagated at a 20-km distance using the amplitude of the gradient, i.e. additional wet delay equal to the multiplication of gradient by the distance. The pseudo-SLANT_GPS in direction of GPS satellites are estimated using isotropic mapping function (GMF in this case; see [37]) and considered in tomography calculations, as illustrated in Figure 5. Note also that 2 other pseudo-stations located at 10 km of the station have been used, considering gradient orientation and its opposite direction. This makes a total of 4 pseudo-sites with 4 sets of additional pseudo-slants (only 2 additional sets is illustrated in Figure 5).”

No need to add this description in Appendix.

This is actually very good point, and the answer depends on the model: BIRA (Appendix A) uses C_M which weights the apriori data according to their uncertainness, similar way the apriori model is introduced (Appendix D). Other models like WUELS, VSB, UBI, does the not use weights.

BIRA is in blue.

The following text has been added in l.692-693 of the new manuscript. Over 6 km the RO profiles is outside the inner tomography grid. For this reason, only RO and NWP shows estimates of N_w over 6 km in Figure 13 (of the new manuscript).

We thinking using our strategy to another case study is relevant. Section 6.1.2 is now dedicated to the use of pseudo-observations in GPS tomography. The figures 17 has been moved in this section (now new Figure 9). This illustrates well the interest of using the new methodology (pseudo-observations) for another case of severe weather.

The authors thank Reviewer 3 for this report which improves the manuscript.

Reviewer 4 Report

Generally, the manuscript represents some interesting aspects of several variant’s impacts on the quality of tomographic results. The article presents a comprehensive investigation on tomography models comparison and methodological improvements to face the limitation of GPS tomography. Thanks for the opportunity of learning your work. Your paper is well structured and readable with adequate information to follow each section. I suggested you a few minor points to be answered and improved.

Line 151: replacing the current legends with higher resolution legends is suggested.

Line 166 and line 201: The authors claimed that pressure retrieval for GPS CORS was done by using interpolation on pressure field of ACCESS-A NWP. If you consider the altitude difference in the interpolation as figure 3 shows the altitude difference in the region is relatively high.

Line 182: For the isotropic and anisotropic components the same symbols are used.

Eq (1): L wet (sym) is not explained. The same comment is applied for the explanation of components in Eq (2), (3).

Eq (6): ds is not defined.

Section 6: In your recommendation for future applications it is not clear if using the 30 min stacking data or pseudo slants can improve the results in all altitude layers?

Line 701: what is the best apriori to obtain the best results for tomography tests? It is not clear in this section.

Author Response

Line 151: replacing the current legends with higher resolution legends is suggested.

The size of picture Figure 2 has been increased and this is now easier to read it.

Sorry the text was not clear enough. Here the new text (l.178-181 of the new manuscript):

"The ground pressures and temperatures of the 4 surrounding ACCESS-A grid points of a GPS station have been converted to the altitude of the GPS site (using hypsometric equation and linear vertical interpolation, respectively). Then pressures and temperatures at the location of the GPS site are obtained using bi-linear horizontal interpolation."

Line 182: For the isotropic and anisotropic components the same symbols are used.

Thank you this has been corrected.

Eq (1): L wet (sym) is not explained. The same comment is applied for the explanation of components in Eq (2), (3).

Components of Eq.2 are explained in the modified l191-192 of the new manuscript:

The isotropic SWD (L_sym^wet) is obtained by mapping of the ZWD using a wet mapping function mf_sym^wet(in our case GMF from Boehm et al. (2006) in direction of the GPS satellite in view above 5° elevation (Eq. 2).

Components of Eq.3 are explained l194.-197 of the new manuscript.

Eq (6): ds is not defined.

The following text has been added in l.212-213 of the new manuscript: “ds is the differential distance along the slant path travel of GPS signal.”

Section 6: In your recommendation for future applications it is not clear if using the 30 min stacking data or pseudo slants can improve the results in all altitude layers?

A new Figure has been added in final section 8 which summarised all the tests. The following text has been added:

"The mean and best results highlight the recommendations of using 30-minutes stacking or pseudo-observations for the layer 0-8 km. The use of combined stacking and pseudo-observations shows consequent instability in the solutions of the three of the tomography software considered. This is due to the high number of data inputs ingested by tomography models and an unsatisfied adjustment for the top layers of the tomography grid. For this reason the overall mean result of the layer 8 - 13 km does not show improvement by using stacking and pseudo-observations.

Line 701: what is the best apriori to obtain the best results for tomography tests? It is not clear in this section.

The answer is in l776-779 of the new manuscript:

“The tests of apriori condition on tomography show that the best results (with respect to RS) are obtained using the best apriori. This is why, assuming that ACCESS-A apriori was reasonably good (and close to RS profiles), tomography retrievals, using regular apriori from NWP, obtain the best results”.

The authors thank Reviewer 4 for this report which improves the manuscript.

Round 2

Reviewer 2 Report

The Authors remarkably improved the quality and readability of the manuscript.

The abstract has been changed, the consistency of the equations has been increased, the quality of the figures has been enhanced, and the structure of the paper is now more clear and concise.

In my opinion, the paper can be accepted for publication in Remote Sensing.

Some informal expressions can be removed at the typesetting , e.g., “it doesn’t” line 764, huge brakes at lines 660, 662. The matrices in equations are not bolded now, however, the bold font is still used for some expressions in text, e.g., line 903, 907, etc.

Line 98 “sometimes few hours” – did you really mean “few hours = the insufficient number of hours” or did you mean “a few hours = several hours”. The same line 53 “horizontal resolution of few kilometres” should be “a few”, line 829 “up to few centimetres”.

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