We sincerely appreciate your valuable suggestions. The author has carefully revised the manuscript based on your feedback, and the modifications have been incorporated into the updated version. Below, we provide detailed explanations regarding the issues you raised:

• In the text, we have supplemented the description of using the Sun as a celestial body for measurement, referenced the work by Danijel Sugar et al., and enhanced the introduction to astronomical observation methods.
• The process of installing two GNSS devices on the straight line formed by the telescope and the azimuth mark is supplemented in the text. The detailed procedure is as follows: First, set up the theodolite on the observation pillar inside the observation room, and precisely adjust it to ensure the instrument's center aligns perfectly with the pillar's center. Then, perform meticulous theodolite leveling. After leveling, aim at the azimuth marker through the theodolite’s telescope, and once the crosshairs coincide exactly with the azimuth marker's center, lock the theodolite’s horizontal circle at this position (while keeping the vertical circle freely rotatable). Next, mount the leveling base and GNSS target on a tripod, employing a two-person coordination method—one moving the tripod and the other observing through the theodolite's telescope. Position the tripod within the telescope's field of view, then gradually adjust its placement until the GNSS target infinitely approaches the line defined by the crosshairs and the azimuth marker. Secure the tripod afterward. At this point, adjust the leveling base. After leveling, the GNSS target may deviate from the line, requiring another fine adjustment to realign the marker, followed by re-leveling. This cycle must be repeated multiple times until the base is perfectly level and the GNSS target precisely lies on the line. Only after fulfilling these conditions can the GNSS receiver be mounted on this tripod system. The same procedure is applied to the second tripod. Ultimately, ensure the four elements are rigorously collinear.
• Due to the incomplete description of this work in the paper, there may be some misunderstandings. The original intention of this paper is not to compare which measurement method is superior. Instead, it focuses on the current task to be completed (the re-measurement of azimuth angles at 45 geomagnetic observatories across our country). Through comparison, we aim to illustrate which measurement method—whether in terms of time cost, convenience, or economic cost—is more conducive to completing this task, leading to the selection of the GPS method. Subsequently, we describe several possible scenarios encountered when using this method for measurement. This does not imply that this method is superior to others. We have added more detailed explanations to this section in the text. They are “In the re-measurement work of azimuth markers at geomagnetic observations in Geomagnetic Network of China, we have chosen the GNSS differential positioning technology. The Geomagnetic Network of China comprises 46 geomagnetic observatoties, and most of them have been in operation for over 10 years. The marker’s azimuths of the early-constructed observatories were measured using traditional astronomical methods, and usually obtained during the station construction period. At that time, the observation rooms were not yet roofed, and theodolites could be set up directly on observation pillars to achieve unobstructed visibility of Polaris. Today, however, the rooms have been fully roofed, making it impossible to see the sky from inside. Moreover, the fixed marker pillars outdoors vary in shape (as shown in Fig.3), and are mostly unsuitable for mounting theodolites on them. Furthermore, traditional astronomical observation is highly dependent on weather conditions. Due to the diverse geographical locations of the observatories, especially those in coastal areas, where cloudy weather is frequent It sometimes often takes several days of waiting for suitable weather to conduct astronomical method, making the measurement process time consuming and inconvenient for arranging remeasurement plans. Therefore, after considering factors such as measurement scenarios, time cost, and operational convenience, the GNSS differential positioning method was selected to complete the remeasurement work.”
• Figure 2 is a schematic diagram of the hour angle method for observing Polaris. To enhance clarity, the revised version substitutes the original partial figure with a complete one, where S denotes Polaris and P represents the North Pole. Corresponding descriptions have also been added in the text. They are “Figure 2 shows the spherical triangle ΔZPS used to calculate the azimuth of Polaris. Based on the altitude angle h of Polaris in the horizontal coordinate system, the latitude 𝜑 of the observation point, the declination 𝛿 of Polaris, and its hour angle 𝑡, the formula for calculating the celestial azimuth A (with the positive direction being eastward from north) can be derived using spherical trigonometry:”
• The content and data regarding GNSS multipath effects have been supplemented in the text. “they may be affected by the multipath effect (e.g., increased errors near water surfaces, glass curtain walls, and metal reflective surfaces). According to actual observation data, the maximum GPS positioning error caused by the multipath effect can reach 3.4 cm (Fu, 2004). In high-reflection environments, this error can be as large as 15 cm (Wang, 2000). When the distance from a high-reflection surface is approximately 50 meters or more, the multipath effect can basically be neglected (He, 2010).”
• Other suggestions (L14, L40, L73, L86, L93, L96, L106, L110, L177, and L179) in the original manuscript have also been revised one by one in the text.

Finally, we would like to express our sincere gratitude for the constructive suggestions provided on this paper. Thank you!

We appreciate the constructive suggestions provided by the reviewers. Based on these feedbacks, we have revised the original manuscript, including modifications to the article title, the rationale for adopting GNSS measurement methods, GNSS measurement errors, the discrepancies between GNSS azimuth angles and those measured by astronomical methods, figure captions, textual expressions, and other aspects. Additionally, we have supplemented relevant content and discussions. The next are the response to the reviewers' comments, and these revisions have been incorporated into the original text, marked in red for clarity.

• Since the work presented in this paper focuses exclusively on China's geomagnetic observatory network, the "In China" was added to the article title.
• The authors have supplemented the rationale for adopting the GNSS method in the re-measurement within the text. They are “In the re-measurement work of azimuth markers at geomagnetic observations in Geomagnetic Network of China, we have chosen the GNSS differential positioning technology. The Geomagnetic Network of China comprises 46 geomagnetic observatoties, and most of them have been in operation for over 10 years. The marker’s azimuths of the early-constructed observatories were measured using traditional astronomical methods, and usually obtained during the station construction period. At that time, the observation rooms were not yet roofed, and theodolites could be set up directly on observation pillars to achieve unobstructed visibility of Polaris. Today, however, the rooms have been fully roofed, making it impossible to see the sky from inside. Moreover, the fixed marker pillars outdoors vary in shape (as shown in Fig.3), and are mostly unsuitable for mounting theodolites on them. Furthermore, traditional astronomical observation is highly dependent on weather conditions. Due to the diverse geographical locations of the observatories, especially those in coastal areas, where cloudy weather is frequent It sometimes often takes several days of waiting for suitable weather to conduct astronomical method, making the measurement process time consuming and inconvenient for arranging remeasurement plans. Therefore, after considering factors such as measurement scenarios, time cost, and operational convenience, the GNSS differential positioning method was selected to complete the remeasurement work.”
• The reviewed manuscript supplements a discussion on the discrepancies between azimuth angles derived from astronomical methods and those obtained through geodetic methods. Empirical data from practical work is utilized to quantify the errors between these two approaches. Based on this, we further analyze the potential errors in our measurement results. The specific supplementary content is as follows: "It should be noted that the azimuth obtained by the astronomical observation method is referenced the plumb line, while the azimuth obtained by the geodetic method (derive from the GNSS method) is based on the ellipsoidal normal. So the vertical deflection introduces systematic error to the azimuths (Vittuari et al., 2016). Account for the influence of vertical deflection, it is necessary to apply the Laplace azimuth equation to convert the astronomical azimuth to the ellipsoidal normal based azimuth (Torge, 2001). Due to the lack of astronomical latitude and longitude values for the measured points, it is temporarily impossible to conduct this calculation. However, previous measurement results can serve as reference for evaluation. For example, Šugar et al. (2012) compared azimuths obtained from astronomical methods and GNSS measurements, finding an average difference of 0.8″, and the standard deviation of the astronomical azimuth was ±2.6″. Based on 14 astronomical observations and comparative experiments with GNSS, Wang et al. (2001) reported that the differences between the two methods mostly ranged between 0–3″, with a maximum difference of up to 4.5″.”
• When two GNSS markers and the azimuth target are aligned in a straight line, the distances from these markers to the observation pillar are unequal. However, by adjusting the telescope focus of the theodolite, the crosshairs can be precisely aligned with the target point. Consequently, the difference in distance between the markers and the observation pillar has minimal impact on the measurement results. The primary source of error stems from the alignment operation of the crosshairs and the target. When the two markers are approximately 200 meters apart, the resulting error is about 1″. Therefore, the distance between the GNSS markers and observation pillar has negligible effect on the results. As long as the distance between the two GNSS points is sufficiently large and the telescope crosshairs are strictly aligned with their targets, the error can be minimized. Additionally, we have added a detailed procedure for aligning the crosshairs with the target in the original manuscript, which involves iterative adjustments.
• The observation room floor is typically elevated relative to the outdoor ground. When observing from the observation pillar inside the room towards the outside, the two GNSS markers usually do not obstruct each other. However, if mutual obstruction between GNSS markers occurs, although the two markers can be aligned onto a straight line (i.e., aligning the distant marker first, followed by the near one), this method is not adopted in actual measurements. The reason is that once one marker is obstructed during measurement, real-time verification of alignment becomes impossible. Therefore, when obstruction occurs, Method Scenario I is no longer applicable, and Method Scenario II or alternative measurement scenarios may be chosen instead.
• For Figure 4, detailed explanatory text has been added in the text.“As shown in Fig.4, images illustrate the alignment process from the observation pillar to the GNSS targets and the azimuth marker. Figure 4(a) demonstrates azimuth marker alignment‌: After precisely centering the azimuth marker using the telescope crosshairs, the horizontal circle should be locked in place. Figure 4(b) shows ‌initial positioning‌: The tripod with the GNSS target should be aligned with the sightline formed by the telescope crosshairs and the azimuth marker. Figure 4(c) depicts ‌the first aligned GNSS receiver‌, while Figure 4(d) presents ‌the second aligned GNSS receiver and azimuth marker‌.”
• Yes, in addition to the distance requirements between the two GNSS markers, factors such as multipath effects and potential obstructions cannot be overlooked. These aspects also require attention during measurements, and the author has included additional explanations regarding multipath effects in the article. “They are easy to operate and can work around the clock, but their performance is poor in environments with insufficient signal coverage or obstructions, and they may be affected by the multipath effect (e.g., increased errors near water surfaces, glass curtain walls, and metal reflective surfaces). According to actual observation data, the maximum GPS positioning error caused by the multipath effect can reach 3.4 cm (Fu, 2004). In high-reflection environments, this error can be as large as 15 cm (Wang, 2000). When the distance from a high-reflection surface is approximately 50 meters or more, the multipath effect can basically be neglected (He, 2010).”
• During the measurement of Scenario 4 at Yulin (mislabeled as Scenario 3 in the original text), the distance between the two GNSS points was approximately 60 m, which may be one of the reasons for the significant error. When using GNSS for measurements, we collected three sets of data and checked the alignment in each measurement. Now, the standard deviation of the three GNSS solutions was added to the result table (Table 2). At the same time, a description of the differences between the astronomical azimuth and the geodetic azimuth measured by GNSS was supplied. And detailed explanations and discussions were given on the final results and the reasons for the large measurement errors in Yulin's scenario 4. They are “Most of the differences between the re-measured azimuths and the original astronomical azimuths are within the range of 0-9″, that is consistent with theoretical expectations. It should be noted that the azimuth obtained by the astronomical observation method is referenced the plumb line, while the azimuth obtained by the geodetic method (derive from the GNSS method) is based on the ellipsoidal normal. So the vertical deflection introduces systematic error to the azimuths (Vittuari et al., 2016). Account for the influence of vertical deflection, it is necessary to apply the Laplace azimuth equation to convert the astronomical azimuth to the ellipsoidal normal based azimuth (Torge, 2001). Due to the lack of astronomical latitude and longitude values for the measured points, it is temporarily impossible to conduct this calculation. However, previous measurement results can serve as reference for evaluation. For example, Šugar et al. (2012) compared azimuths obtained from astronomical methods and GNSS measurements, finding an average difference of 0.8″, and the standard deviation of the astronomical azimuth was ±2.6″. Based on 14 astronomical observations and comparative experiments with GNSS, Wang et al. (2001) reported that the differences between the two methods mostly ranged between 0–3″, with a maximum difference of up to 4.5″. Therefore, when considering systematic deviations between astronomical and GNSS methods, positioning errors, sighting alignment errors, and other factors, a discrepancy of 0–9″ is within expected limits. Furthermore, in terms of the accuracy requirement for azimuth in absolute geomagnetic observation (0.1′), a variation of 0–9″ over several decades is considered acceptable. Thus, it can be concluded that no significant displacement has occurred at the observation markers.“  and “However, in the Scenario IV test at Yulin observatory, a significant deviation (>40″) was observed between the measured and original results. Two primary factors may contribute to this result. The first one is the insufficient GNSS baseline length. Despite the RMSE of three measurement sets remained stable at 0.7″, the short distance between two GNSS points (about 60 m) and the maximum horizontal error (about 2.5 mm) may introduce the potential angular error of up to 8.6″. The second one is the theodolite setup error‌. In this scenario, the theodolite needs to be installed on the tripod at point A, as shown in Fig. 8(b). During angle measurement process, a centering offset was detected on the tripod. After re-centering, a change of 10.8″occurred. This underscores the necessity of adequate baseline distances and highlights the need for further analysis of tripod measurement error characteristics.”
• The author fully accepts the other suggestions (L17, L19, L20, L50, L69 in the original manuscript) and has made corresponding modifications at the relevant positions.

Finally, the author expresses sincere gratitude to the reviewer for these questions and constructive comments on this manuscript.

Thank you very much to the editor and reviewers for their review！

Responds to the comments1

The authors have properly made corrections in response to my points. Additionally, they have added the discussion with an attempt to correct the vertical deflection, which is welcome. To finalize the paper, please consider the last points below : 

L285: Account -> Accounting

L288: 2001). -> 2001), 

L290: Where -> where

Reply: These errors in L285, L288, and L290 have been corrected.

L302: The paragraph wouldn't start here.

Reply: This paragraph has been moved up to L281 in front of Table 3. 

Section 5: It is uncommon to have the title "Conclusions and discussion". I suggest that the discussion part (the third paragraph starting from L324) is moved to Section 4 so that Section 5 is dedicated solely for conclusions. Also there is ambiguity in the first sentence of Section 5. Some readers may start with Conclusions, so it is better to clearly describe the "two methods" comparing the azimuths measured in the past and re-measured recently. 

Reply: Thank you very much for your suggestion. The third paragraph of "Conclusion and Discussion" (starting from L324) discusses the results of the re-measurement. Therefore, it would be more suitable to be placed in Section 4. Now this paragraph has been moved to Section 4 (starting from L281). Section 5 only displays the conclusion section.

Responds to the comments2

There is just one comment from Reviewer #2:

It would be better to briefly describe (in Section 4?) how the angle measurements are made with a theodolite (how many repetitions? in both faces?).

Reply: Thanks for the reviewer's suggestion. We have added a description of the number of repeated measurements in Section 4 (starting from L288) and provided the mean square error of the measurement results in Scenario II and Scenario IV. These sentences are “The last one is that measurement errors will be introduced when measuring the angles between the azimuth mark and the GNSS target in Scenario II and IV using theodolite. In this work, each angle was measured 6 times. The standard deviation of angle a in Fig. 3 of Scenario II is 2.5″, and standard deviation of angle a1 and a2 in Fig. 5b of Scenario IV are 3.3″ and 1.8″, respectively.”