General comments:

This study employs tidal gauge and remote sensing data to investigate the statistical characteristics of continental shelf waves in the northern South China Sea. The topic should be of interest to those who focus on the coastal dynamics. I’ve identified some points below which might help. I’m recommending a major revision before it can be published.

Specific comments:

1. According to Wang and Mooers (1976) as well as Brink (1991) and Huthnance (1995), the CSW and ATW referred in this manuscript should be more specified as Kelvin wave and topographic Rossby wave, respectively.

Wang, D., and C. N. K. Mooers, 1976: Coastal-trapped waves in a continuously stratified ocean. J. Phys. Oceanogr., 6, 853-863.

Brink, K. H., 1991: Coastal-trapped waves and wind-driven currents over the continental shelf. Annu. Rev. Fluid Mech., 23, 389-412.

Huthnance, J. M., 1995: Circulation, exchange and water masses at the ocean margin: the role of physical processes at the shelf edge. Prog. Oceanogr., 35, 353-431.

2. The description of wavelet analysis in section 2.5 is not necessary because it is a method widely used in different studies.

3. By the way, it should be better to describe the theory of CSWs in section 2 rather than in section 4.

4. The EOF analysis may be a better tool to reveal the principal modes in Figs. 3 and 8.

5. The boundary conditions should be given in sections 4.1.1 and 4.1.2.

6. Fig. 4 could be omitted because it is not helpful for the analysis and there are also few descriptions about it in the manuscript.

7. Since the authors have realized that the discrepancies in Fig. 7 may be owing to the wind forcing and baroclinicity, they had better include these effects in Eq. 6 and show the relevant dispersion curve for comparison.

8. The results shown in Fig. 9 suggest that the assumption at L260-264 is not proper for the reality.

Technical corrections:

1. L336: it should be (24).

Review of “Statistical analysis of dynamic behavior of continental shelf wave motions in the northern South China Sea”

Using a combination of tide-gauge and along-track altimeter data, this study examines the cross-shelf structures of continental shelf waves (CSWs) and arrested topographic waves (ATWs) in the northern South China Sea (SCS). I think it is very interesting to isolate CSWs and ATWs from observations according to their respective dynamics. The manuscript is overall well organized. In particular, I like the dynamic analysis illustrated in Section 4 and fitting the theoretical solutions to observed profiles. However, I think the manuscript could be further improved subject to taking into account several issues detailed below. I suggest a Major Revision in this round of review.

1. Introduction. Instead of very broadly describing sea level variations in the SCS and their relationship with for example ENSO, I think the authors should get quickly to the core content focused in this manuscript. For instance, the authors can review relevant studies on CSWs and ATWs in the China Seas or in global shelf seas, summarize the state-of-the-art understandings of general dynamics and regional oceanography, and propose outstanding issues particularly the ones that will be addressed in the present study. Also, listing a number of studies as in the second paragraph of Introduction is not an ideal way to summarize current understandings; rather, they should be organized in a sound and logic way.

2. Section 3.1 & Fig. 2. The authors identify sea level signals with periods shorter than 40 d as CSWs while those longer than 40 d as ATWs, and state that they “show remarkably different characteristics”. However, the remarkable difference is not clearly discernable from Fig. 2. In particular, I do not see evident discontinuity around the period 40 d in Fig. 2b. The authors need to illustrate more clearly what specifically the “remarkably different characteristics” Moreover, instead of showing all the resolved periods in a single panel, I suggest plotting certain period bands of interests in different panels with enlarged views of the details and adding auxiliary lines when needed to illustrate for example the content in L168-170.

3. This is related to the previous comment. I think the governing equations and wave solutions derived in Section 4 are more clearly for CSWs than for ATWs. This could be overcome by indicating ATWs more explicitly in Section 4.2. For example, making subsection titles of Section 4.1 and 4.2 more parallel (e.g., “Governing equations and wave solutions for CSWs/ATWs), explicitly indicating Eq. (21) is the solution for ATWs and Fig. 6 is the theoretical ATW profiles (rather than “normalized SSH ...”), etc. This would also help readers to more easily understand what theoretical ATWs refer to as described in L482.

4. L188-190. I understand that the China Seas are overwhelmed by northeasterly in winter and by southwesterly in summer. But coastal trapped waves (CTWs) should propagate equatorward (with the coast on the right side) in any season. How come seasonal signals at Xiamen would lead that at Kanmen in summer? In which form of coastal waves would sea level variability propagate poleward from Xiamen to Kanmen? Normally when wind direction is opposed to the propagation direction of CTWs (in summer for China Seas), alongshore wind would play a limited role in regulating coastal sea level variability downstream (in the sense of propagating CTWs).

Minor ones:

1. Lower, not higher, percent values of significant level mean more significant.    So here I think it is “larger than”instead of “less than”.

2. L246-247. The “long-wave assumption”seems to assume that the cross-shelf length is much smaller than along-shelf length (l/L<<1). Why would it lead to du/dt=0?

3. Fig. 4 is not referenced in the main text.

4. L483-484. Descriptions in these two lines only apply to Track 12. Is this correct? If yes, this needs to be illustrated more clearly in the texts.

This paper examines sea-level variability in the South China Sea by using tide gauges and satellite altimetry data. The signals are interpreted as continental shelf waves (CSWs) and arrested topographic waves (ATWs). The submission reviewed many previous studies on sea level in the South China Sea, and aim to (1) extend observations offshore and among the tide gauges, and (2) resolve periods shorter than 10 d (the satellite orbit period). These aims are partially accomplished, but the analysis and presentation could be improved and clarified.

Minor comments:

(1) Line 108-111, there are two types of along-track SLA, i.e., SLA_unfiltered and SLA_filtered. Please clarify which kind of data in this submission has been used.

(2) Line 112, it is very important to discuss the availability of along-track SLA in the coastal zones.

References:

Birol F et al.. 2021 The X-TRACK/ALES multi-mission processing system: new advances in altimetry towards the coast. Adv. Space Res. 67, 2398-2415

Vignudelli S, Birol F, Benveniste J, Fu LL, Picot N, Raynal M, Roinard H. 2019 Satellite altimetry measurements of sea level in the coastal zone. Surv. Geophys. 40, 1319-1349.

(3) Fig. 3, give cross-shelf scales consistently in km instead of degree.

(4) Line 273, add Robinson (1964) shelf wave theory.

(5) Line 279, the simplified bathymetry in the analytical model is not very realistic in the the bathymetry of the SCS, especially in the deep ocean part. Why not use more complicated bathymetry, or realistic bathymetry by using a tool from Brink and Chapman (1985).

Brink, K. H., & Chapman, D. C. (1985). Programs for computing properties of coastal-trapped waves and wind-driven motions over the continental shelf and slope. Woods Hole Oceanographic Institution.

(6) Fig. 6, add a decay scale of the Rossby radius of deformation.

(7) Fig. 7, lacks error bars.

(8) Data in station Kanmen was not discussed in this manuscript.