General comments:

Zhou et al. present in their manuscript a framework to determine the migration rate of drainage divide and apply the methods to two study cases in the Wutai Shan and Loess Plateau. The authors developed new methods of drainage divide migration rate estimation using high-topographic data based on channel-head parameters,  values of channel segments, and erosion rate parameters. They argue that by determining the exact location of the channel heads, the migration rate of drainage divide can be accurately calculated. They determined drainage divide migration rate of about 0.10-0.13 mm.yr^-1 and closed to zero for the Wutai Shan and Loess Plateau study cases. Finally, they suggest that the difference in uplift on both sides of the drainage divide have to be considered in order to calculate drainage divide migration rate with this method.

The topic of drainage reorganisation by drainage divide migration or river capture is receiving increasing attention these years. Therefore, this contribution, which determined the rate at which drainage divide migrate, is timely and should be of interest to the EGUsphere journal. This study also presents a nice follow-up of drainage divide migration estimation to the study by Zhou et al., 2022 (although I find the two manuscripts really close). The manuscript is interesting and overall well-written. The provided model, methods and equations in the manuscript are sound and well-used in the study area cases. There are a few awkward sentences that I have indicated below. Finally, I found the figures well realized and easy to understand.

My main comments/concerns regarding this manuscript are the use of strong assumptions made in the calculation of the drainage divide rate migration which have not been mentioned in the main text. The first one is the use of erosion rate estimate from low-temperature thermochronology data, which cannot correspond to a modern rate for the Wutai Shan study case. The second is the systematic use of a “standard” concavity index for both study cases. I feel like these assumptions have to be addressed. Since the main message of the study is to quantify migration rate from high-resolution topographic data, estimation of the equation parameters needs to follow the same logic.

More specific comments tied to line number:

Specific comments:

• Line 37-39: “The evolution of topography is fundamentally coupled with changes in drainage systems, including river’s vertical and lateral movements”. Can you be more precise about vertical and lateral movements? Maybe add river capture as another important process for drainage changes.

• Line 70-71: “For example, Willett et al. (2014) developed the χ method to map the dynamic state of river basins”. I don’t think Willet et al (2014) developed the χ method. Please change the term “developed” by “applied” or cite “Royden et al., 2000; Perron and Royden, 2013” instead.

• Line 79-81: “Zhou et al. (2022a) developed a technique to calculate the migration rate through the cross-divide χ ratio of high base-level channel segments”. This statement is in contradiction with line 78 “No rates have been obtained”.

• Line 89-90: “to obtain the high-resolution topography data of these two areas”. Can you precise the resolution of your topography data here or somewhere in the manuscript.

• Line 98: “Moreover, benefiting from the detailed tectonic research”. Please reformulate or precise what is this “tectonic research”.

• Line 127-128: “A large erosion coefficient also creates a high channel-head erosion rate”. This sentence is unclear. What does the term “erosion coefficient” refer to?

• Equation 4: This equation is correct only if the erodibility is the same on both side of the drainage divide. Correct the equation or precise this assumption in the text. This is important, especially, since you demonstrate in your Figure 1 that the erodibility affect the channel-head erosion rate.

• Line 184-185: integral function of channels’ upstream area (A) to horizontal distance (x) (Perron and Royden, 2013; Willet et al., 2014)”. Replace the reference “Willet et al., 2014” by “Royden et al., 2000”.

• Line 241: “If we assume the rock uplift rate decreases linearly from 0.25 to 0 mm/yr from northwest to southeast of the Wutai Shan horst”. If I understood correctly the 0.25 mm/yr rate come from the low-temperature thermochronology study. Even if this rate is predicted for the late Cenozoic, it cannot reflect the modern erosion rate (the method is not sensible) needed to accurately calculate the modern drainage divide. It assumes that the erosion rate stayed constant. This assumption is not reported in this paragraph or the discussion.

• Line 246: “We assume n = 1 and m = 0.45 in the calculation following previous studies (Wobus et al., 2006; DiBiase et al., 2010; Perron and Royden, 2013; Wang et al., 2021)”. This is a reference concavity of 0.45 that you are using for your calculation. How does this concavity really reflect the geomorphology of your study area? There is available framework to calculate the channel concavity of your catchment, check Mudd et al., 2018. This is even more important since you can have different concavities on both side of your drainage divide and strongly affect your migration rate calculations based on your equations.

• Line 313: “We also assume n = 1 and m = 0.45 in the calculation”. Same as previous comment.

• Line 294: “An unnamed mountain range in the Loess Plateau”. The term “unnamed” sounds strange. I suggest to just remove it or find another solution.

• Figure 1: It might be better to directly indicate the value of in the different panel instead of the ratio. You can also precise the erodibility for each panel in the figure description since you did it for the slope and area coefficients.

• Figure 2: Precise the meaning of the white rectangle in the description like for the back rectangles.

• Figure 4: The text of Eq. 4 and 8 could be coloured in black and blue respectively in order to directly identified which arrows correspond to which equations and rates. Or you could add small arrow legends on the left of the text.

Technical corrections:

• Line 60-62: “However, these techniques are usually based on samples collected from an outlet that is several kilometers away from the drainage divide and thus may not represent the erosion rates close to the drainage divide”. Change “an outlet” to “a catchment outlet”.

• Line 65-67: “Hence, it would be ideal to find an accessible and efficient method that can be applied to the entire landscape and cross-checked to make full use of the ¹⁰Be-derived erosion rates”. The term “cross-checked” is unclear in this sentence.

• Line 68-69: “The advancement of remote sensing technology has promoted the development of geomorphic analysis theory”. Remove the term “theory”.

• Line 77: “No rates have been obtained”. This short sentence might be combined with another one.

• Line 86: “an unnamed mountain range in the Loess plateau”. Remove the term “unnamed”.

• Line 128-129: “The results indicate that the side with a higher A_cr or S_ch can have a higher erosion rate than the other side of the drainage divide”. Move the terms “of the drainage divide” to the first occurrence of the term “side”.

• Line 134-136: “when one uses the cross-divide erosion rates … one should also consider the influence of differential uplift rates”. I suggest to remove the terms “when one” and “one should” and reformulate the sentence.

• Line 144: “Combining Eqs. 2 and 3, one can derive the equation”. Same as previous comment, replace “one can” by “allow to” for example.

• Line 216-217: Correct to “The bedrock of the Wutai Shan area consists mainly of metamorphic and igneous basement rocks”.

• Line 263: Change to “Figure 3. Topography (A) and normalized channel steepness (ksn) (B) distribution”.

• Line 264-265: The black dashed curve shows the location of the main drainage divide”. Change the term “curve” to “line”.

• Line 272-273: “The topography swath profile along E-E’ in Fig. 3A. (D) The ksn swath profile along F-F’ in Fig. 3B”. Change the terms “Fig. 3” to “panel”.

• Line 273-274: “The red dotted line shows”. Correct to “The red dotted lines show”.

• Line 279-292: Replace the terms “curve” by “line”.

• Line 292: Correct to “the channel-head (Eq. 4) and channel-head-segment (Eq. 8) methods respectively”.

• Line 296: “(Yin, 2010 Su et al., 2021)”. There is a missing coma between the two references.

• Line 306: “the slope-area plots (Figs. 5 B, E, H) and the χ values”. Change “and” by a coma.

• Line 324-334: Replace the terms “curve” by “line”.

• Line 346-347: “In the tectonically active area”. Change “the” by “a”.

• Line 350-351: Zhou et al. (2022a) combined the advantages of the χ and Gilbert metrics methods, proposed to use the χ contrast with a high base level”. This sentence does not sound right. Maybe change “combined” by “by combining”.

• Line 361: “(Forte and Whipple, 2018; Zhou et al., 2022a; this study)”. Remove “this study” to the references.

• Line 363-366: “In this study, we advocate the use of high-resolution DEM to determine a more accurate position and related parameters of the channel head, given that the use of UAVs to obtain the local DEM has become highly efficient”. I suggest to break this sentence in two (maybe around the coma).

• Line 368-369: “one can obtain the sub-meter resolution topography data of drainage divides”. Replace “one can” by “it is possible to”.

• Line 396-397: Change “Consider an extreme example: when the main drainage divide” by “If we consider an extreme example where the main drainage divide”.

This study addresses a highly pertinent question that lately has garnered significant attention in the scientific community focused on landscape evolution: what are the rates at which drainage divides migrate? The study presents two quantitative methods for measuring migration rates, both of which necessitate precisely identifying channel heads through high-resolution DEMs. The first method leverages the channel head's area and slope, while the second method builds upon an enhanced version of Zhou et al.'s (2022) technique, incorporating χ values, elevation at the channel head, and outlet elevation. The study applies these two methods in two distinct field settings—one impacted by tectonic tilting and the other situated in a tectonically quiescent area. The results reveal a similarity between the outcomes of both methods, suggesting that in the tectonically affected area, the divide is migrating in rates of ~0.1 mm/yr, while in the second setting, the divide is stable.

The foundational concept of the study seems promising, and the paper's structure effectively guides the reader through the core idea. Nevertheless, there are several crucial issues that demand the authors' attention, particularly regarding the methods presented in this manuscript. Hereafter I highlight specific points that warrant further clarification and elaboration.

Overall points:

1. In the introduction, I recommend the following improvements: A) Provide a more in-depth motivation regarding the significance of divide migration, emphasizing its relevance to different studies. B) Distinguish between field-based investigations involving natural cases, such as those using cosmogenic nuclides and thermochronology, and modeling-based approaches, which use χ or Gilbert methods. C) Expand upon the method introduced by Zhou et al. (2022), elucidating how it forms the foundation of your research.
2. The terminology "channel head method" and "channel head segment method" might confuse readers. I recommend considering alternative names for one of these methods.
3. The channel head used in equations 5-7 defines a point that separates the hillslope from the channel. However, the calculation of slope inherently involves two points. Therefore, it is essential to elucidate how you measured the slope in this specific context, particularly within the channel head, where it distinguishes between areas with differing slopes.
4. I think it is crucial to provide a clear mathematical definition of parameters χ and k_sn which are employed consistently throughout the study. Additionally, an explicit explanation of how Equation 8 was derived would be valuable. I am asking because k_sn pertains to a specific point in the channel while χ represents an integral over a channel segment.
5. The calculation of the regional erosion coefficient K in this study requires some further clarification and consideration of several points: A) in the case of the Wutai Shan area, it is assumed that rock erodibility and precipitation are uniform. How is this assumption valid in a landscape with a range of elevation ranging between ~100-3000 m? Consider including isohyet maps and geological maps to strengthen your argument.  B) You mention that the erosion rate you used in the study averages a long time frame (since the late Cenozoic). However, the k_sn values, that are also used to calculate the erosion coefficient K, are based on the present conditions of lithology and precipitation. Do you think the k_sn values also remained uniform since the late Cenozoic? Please explain the feasibility of these assumptions in the text. C) It is unclear why kriging interpolation is required over all of the landscape, as K_sn values are relevant only across channels. D) One value of erosion rate was considered for calculating the K of all the Wutai Shan area. However, the erosion rates along a tilting block might vary and probably decrease with distance from the northern Wutai Shan fault.
6. Errors and Uncertainties: Including error estimates and uncertainties in the study is crucial. These include horizontal and vertical errors of the DEM data and uncertainties related to slope measurements, erosion rates, and k_sn Please explain how these errors propagate into the migration rate calculations and discuss their implications for the study's findings.
7. Accessibility and resolution of the data: Please provide the precise resolution of the DEM and not only a general "sub-meter" description. If possible, include these DEM datasets as supplementary materials or explain any limitations or reasons why they cannot be
8. Maybe evaluate the relevance of Section 4.1 and consider incorporating it into the introduction. Currently, in my opinion, it fits to the introduction, as it provides motivation for the study rather than introducing new information.
9. Can you identify morphological evidence from the field that supports the inference of drainage divide migration? For instance, wind gaps along the divide or evidence for stream capture? Such evidence can meaningfully support your results.
10. I provided some suggestions for edits that can assist in the flow and structure of the manuscript, such as connecting too short sentences e.g. lines 293, repetitive sentences, e.g., lines 54 and 132, or unclear sentences such as 251-252.

Line-by-line comments:

20: "normalized channel steepness"- I don't think this term can be used in the abstract without explanation.

22: Maybe give these mountains a name of your own, as you refer to them several times in the manuscript. Same for line 86 and further in the manuscript.  

23-25: I suggest connecting these two short sentences to one sentence, e.g., "Our results find that the divide in Wutai Shan range is migrating north in a rate of between 0.10 to 0.13 mm/yr, whereas the migration rates at the mountain range in the Loess Plateau are approximately zero."

25-27: How is this demonstrated?

34: "…providing a basis.."

37: What is the difference between the evolution of earth's surface and the evolution of topography?

38-39: The sentences imply that there are other changes in drainage systems that are not included in the river's vertical or lateral movements. If yes, what are they?

40-43: Maybe write shortly about the findings of all these investigations.

44: Why however? i.e., how does this sentence contrast with the previous one?

47: I think you must define here what is drainage divide migration.

47-51: It is unclear why and how the divide migration carries information about the disturbances and the tectonic information extraction.

55: The migration is also controlled by the topographic slope in the citations you provided.

59: In what cases do you use migration velocity, and when do you use migration rate? Same for line 79, 145 and further in the manuscript.

63: Do you mean "..of sample processing"?

65 and 66: Perhaps replace "entire landscape" with "large landscapes" or alike. It is not clear to which entire landscape you are referring to.

68: The term "remote sensing" includes a very wide range of data types. Maybe be more specific.

69-70: What do you mean by "determine the drainage divide's motion through topography analysis "? determine the past motion (i.e., infer divide migration that occurred in the past)? Or predict future motion?

71: See overall comments- you should explain more about the χ parameter and devote an equation to this, especially if you use it in your equations later.

73: What do you mean in determine a drainage divide motion? The direction? Rate?

74: What is the difference between slope angle and the slope mentioned in the previous sentence?

75-77: The fact these methods are quantitative does not necessarily mean they can provide rates. No need to add the contrast term "although" in the beginning of the sentence.

78: Please explain better about this "method". I assume you mean he used numerical simulations. Also, as I wrote in the overall comments, I recommend separating between modelling-based studies and all of the other studies you cite, that are field based.

81-80: Explain "cross-divide χ ratio". Ratio between what and what?

81-84: This sentence doesn't make sense to me. First, something is missing here- you need to mention that the technique of Zhou et al 2022 requires channel head parameters before saying that these parameters are problematic. Second, what are the previous studies you are talking about? Are you referring to a case-specific study? and why this parameter is not applicable in specific natural areas?

85: Before this sentence, I suggest providing the knowledge gap and saying what problem you are addressing (e.g., "Currently, there is no method for quantifying divide migration rates across large landscapes.. ").

91-93: When first reading this, it is unclear how you calculated the migration rates from the parameters. Perhaps write that you developed two methods for this and that one is based on the method of Zhou 2022.

93: When you mentioned the method of Zhou et al. 2022, you didn't say that this method doesn't apply to cases where the elevations of outlets and channel heads are different across the divide (isn't this almost always the case?).

96: This sounds like a good sentence to open the paragraph.

98: Maybe delete "moreover."

99: "Quantify the influence" is not clear to me. Do you mean Quantify the cross-divide difference in uplift rates?

109-111: Landslide threshold and erosion threshold are not mechanisms- they are thresholds. If you mention them, you should explain what these thresholds are, and why do they cause the channels to emerge at a certain distance from the divide.

121: Slope is measured between two points. What are these two points in this case? Do you measure only from the channel head and downstream (because the channel head is the highest point of the fluvial segment)

122-131, including figure 1: I think it is obvious that increasing S, A, and K, or decreasing the m/n ratio, will result in higher erosion rates. Do I miss something here? Please clarify or eliminate this part+ this figure.

132: Repetitive with the sentence in line 54, see comment there.

139: Eq 3 suggests that migration is also a function of the gradients of the slopes across the divide.

142: I think you can delete "rock."

147: I suggest moving this sentence to line 141 where α and β are first presented.

157: Add citation for measuring erosion rates from cosmogenic nuclides

157: Please clarify what is the regional average erosion rate. Do you mean (E_α + E_β)/2 ?

162: It can help to add the symbol, i.e., "erosion coefficient (K).." etc.

173: What do mean by channel head segments? The segment between the divide and the channel head? If yes, better define in the text.

174-176. About K_sn -See comment to line 71 and general comments.

1. This is the missing information for the comment in line 84. Nonetheless, I don't understand how the channel head and the outlet of two channels across the divide can be the same elevation in natural settings.

183: need to explain about χ in the place it first appears (see comment on line 74)

199-206: This reads more as part of the methods, in particular lines 203-206.

208, Fig 2: Beautiful map! Some notes:

-Please provide a source of information for the maps.

-I suggest annotating each map differently (A and B), and refer to them in the captions accordingly.

-Maybe add a legend for the faults. Are they all normal faults? If not, mark them with simple curves without the small lines that stick out.

-How come the highest elevation in the map is exactly 5000 m (should be m asl- above sea level)? If this is not exactly the value, please fix to the correct max elevation in the map.

214: Refer to fig 2.

216: But figure 3A does show a fault in the south (Xizaou chen)? Do you mean that the tilting of the Wutai Shan is dominated mostly by the activity of the northern fault?

218-219: As I wrote in the overall comment 5- how can you explain no variation in precipitation in an area with an elevation difference of ~2500 m?

220-228: Maybe this part can fit better in the methods section. Aside from the comments in overall comment 5, the calculation of erosion coefficient here is not clear unless you provide the equation that relates between k_ns, k , and erosion rates.

224-225: Add a reference to fig 3. Also- is the erosion rate based on all five samples illustrated in figure 3?

230: What do you mean by "randomly"? maybe delete. Same for line 302

231: How did you measure the slope (see overall comment 3)? Was it extracted from the high-resolution DEM? 

232: You probably mean "the breaking point of the slope-area regression line? Was this point determined manually or by an automatic algorithm?  

237: What average- the average slope of all points measured between the channel head and the divide? Also- why do use only the points that are upstream from the channel head? They represent the hillslope section and not the fluvial segment of the channel.  

238-240: I'm not sure I understood from the text: z_b and z_ch  and the χ  values were extracted from the χ plot? If yes, please rephrase for making the text more clear.

243: "The normal direction of the boundary fault"? what does this mean? Parralal or perpendicular to the direction of the fault?

246:  Are you following previous studies that generally used these values or specific studies that used similar values in your study area?

251-252: The sentence "…show that distinct character of the rivers across the drainage divide" doesn't make sense to me. Please try a different phrasing.

259: Suggest adding "in this area" at the sentence's end.

Fig 3: A. cite Clinkscales et al 2020 also in the legend. B. See comment on elevation scale in fig 2- same for the k_sn scale here.

265: Same comment about the faults in Fig 2.

267: Maybe write "Black rectangles show the area of Fig. 4A".

271: I think that "based on matlab" can be deleted.

272: What software did you apply for the kringing method?

273: Did you use topotoolbox also for the swath profile? if yes please mention it.

273: Not dotted, dashed.

275: I recommend showing the extent of the swath profile in figs A&B.

Suggestions to figs. 4 and 5. fig A: i) Specify "profiles" in the legend – I think you mean topographic profiles. ii) Add the arrows and the divide to the legend - maybe make the arrow length proportional to the migration rate. iii) Complete the divide line. iv) Maybe change the scale in the bottom left corner to white. v) I think that you can eliminate m=0.45 and n=1 in the middle columns. V) I am not sure it is right to continue the χ profile up to the divide (ie, upstream from the channel head), as this segment is not fluvial and is not applicable for χ analysis.

280: Please explicitly specify the resolution. Also, this is not a topographic map but a hillshade map. 

292: Should be "methods."

294: Maybe give it a name of your own?

296-7: Please check the grammar and correct accordingly.

298: Maybe connect this short sentence to one of the sentences before or after it.

301-309: This subsection is repetitive with the previous one. Perhaps just write that you extracted the migration rates similar to Wutai Shan site.

1. Is this an average erosion rate? If yes, what timescale does it average? How was this rate extracted? Please elaborate on this.

337: Should be "in the two field cases."

Table 2: The lack of uncertainties here is substantial.

349-350: These sentences are almost similar to those in line 72. As I wrote in overall comment 8, I think that all of this subsection should be merged with the introduction.

355: "These methods"- do you refer to χ, Gilbert methods, or Zhou's? Or all?

362: What are the empirical parameters on which the channel head location relies on? And what is the problem with them? Do you mean that the location depends on the break of the slope, which cannot be determined appropriately in DEMs with a coarse resolution?

363: Perhaps: "which can induce uncertainties in determining the stability of drainage divides".

382: I am confused- you are saying that the differential uplift rate should be ignored or taken into account?

394: You assume that divide migration rate decreases as the divide becomes closer to steady state. Please provide a reference to this argument. However, this also implies that the divide migration rate may change over long timescales. This might not be consistent with the parameters that were used for calculating k (Wutai Shan) or E (Loess plateau), which represent an average over long timescales.