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.

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 SAAS_D for validation? What is the impact of your proposed correction model in SAAS_Z?

Reply to Comment 11. Thanks for your question. We chose SAAS_D just for an example since the difference between the two models is not that large. And we added this explanation at Line 146.