Li et al. compared different methods of correcting 3D-shifts and others biases in digital elevation models (DEM) with the ultimate goal to reduce uncertainties in glacier elevation change estimates. They first compared the widely-used Nuth & Kaab (2011) to the less popular Rosenholm and Torlegard (1988) algorithms for DEM coregistration. On top of a simple 3D shift, the latter algorithm also account for any rotation or scale differences between the DEMs. Further, they proposed an improved correction of the structured-biases between the DEMs that have a proper signature in the two directions of image acquisitions (along and across tracks). They go beyond fit by polynomials and sums of sinusoids by proposing a spline-based non parametric model.

I found nothing wrong with this study. However, I am not super convinced that this article, in its current form, fits well in The Cryosphere and its readership. I see two main reasons for that:

1/ DEM differencing is a popular technique to measure glacier changes. However the scope of the present study is really technical with no direct application to glacier changes. The study sites only marginally include glaciers.

2/ The added value of the proposed method is modest. I am not convinced that a gain of 0.2 m (5%) in standard deviation of the residuals between DEMs only covering a single (and not very challenging) test site is sufficient to convince the glaciological community to rethink the way they coregister DEMs. The added value of the spline-based correction of along track residuals is higher but would need to be confirmed in different settings.

Overall the paper is well written, the work is performed seriously but I missed some novel results that would make a real impact on the glaciological community.

Major comments

1/ Do the conclusions apply in other settings? Map of elevation differences are constructed from several ASTER DEMs in western Greenland with a strong proportion of stable terrain. Ice-covered terrain is restricted to the eastern part of the images/DEM. It seems that images are almost cloud free. This site and the cloud-free images are appropriate to design and test the different methods but are not representative of real case scenario. In my experience, further challenges for DEM coregistration comes from: vegetation (changing with time), large fraction of glacier areas vs. stable terrain, gaps or unreliable data in the DEMs due to clouds, the rough topography leading to higher noise level in the DEMs. Authors did not explore these difficulties and thus their results are not representative of more complex and more realistic situations.

2/ Do the improvements over stable terrain percolate to ice-covered areas? To convince the readers (glaciologists, the readership of TC) of the added values of the proposed methods, authors would need to demonstrate real improvements over glacier terrain. Such a validation is tricky, I reckon, because glacier elevations are constantly changing. I see two ways for the authors to demonstrate this

(a) apply their methods to DEMs derived from images acquired just a few days apart so that the assumption of no elevation change is almost valid. They would then be in position to coregister and bias correct their DEMs over the stable terrain and then check the improvements on glaciers (where no change should be measured over a few days).

(b) find sites where ASTER DEMs are acquired simultaneously to higher resolution DEMs (for example from the Arctic DEM project) so that a reference elevation change map is available. This second solution is more tricky to identify.

3/ The discussion is rather weak. There is a long part about the “extrapolation error” that is mostly unrelated to the rest of the article.

4/ I was also a bit disappointed to see that the techniques are only apply to ASTER DEMs. This also reduce the scope/relevance of the results.

Specific comments

L30. I find it unbalanced that three out of four references on the use of DEMs for glacier elevation change mapping are from Chinese colleagues. Others more seminal papers on the topic could be cited here.

L31. Leprince et al., is about mapping surface displacements (using Cosi-Corr), I am not sure this reference is appropriate for DEM errors. Can authors double check?

L50. What are these "scenarios"?

L71. Authors need to explain why they need to revisit the Nuth & Kaab's method and why they present in details these flavours of their method. It is not straightforward for the reader what is the aim here. Also because in the end the results are almost identical...

Figure 1. I did not really understand the figure because I did not understand what were representing the different letters/segments. Annotation to be clarified.

Figure 2. the terminology "master" and "slave" are not very the best ones for ethical reasons. “Reference” and “secondary” DEMs are better.

L204. I do not understand why 23 DEM pairs are first mention and then only 2 DEM pairs are presented in detail in Table 2. Rather include an appendix with the dates and ID of all the DEMs so that the study can be reproduced. Also, as you read in my general comment, a more extensive study using a variety of study sites would be more convincing.

L208. The NDBI index is not often used in the glaciological community so need to be explained a bit more.

L215. I do not understand how this 3-sigma rule is applied to check outliers from the classification. Authors need to elaborate more.

Figure 4 does not really bring much. I think it will be pretty obvious to most readers and can be explained in a few sentences in the text.

L239. Example of why the application of the algorithm to a greater diversity of images is needed.

L302. English is not really correct I think. Check

L320. This statement (and the rest of the paragraph) about extrapolation error and elevation error as a function of altitude comes a bit out of nowhere. Why discussing extrapolation when this was not mentioned before.

L328. This is exactly what the revised study should do: include cases where bare terrain is rare and see how the different methods compare.

L349. I found the improvements rather modest. “outperformed” is a bit overselling.

This paper deals with the co-registration of DEMs for determining surface elevation changes by DEM differencing. The differences between DEMs are affected by random measuring errors and various systematic errors  due to imperfections of the sensors. The success of the simple differencing method depends on how well the systematic errors can be determined and be removed. The paper begins with comparing 3 variants of the Nuth and Kääb method with the lessor known method proposed by Rosenholm and Torlegard. The authors then introduce a non-parametric residual correction model and present results from a few experiments with ASTER DEMs of Western Greenland.

Major Comments

I agree with the authors that the Nuth and Kääb method is predominently used for co-registering ASTER DEMs by the cryospheric research community. The method has been improved over the years, particularly with handling systematic errors of ASTER DEMs (see reference Luc Girod et al., 2017). If one wants to correct Aster DEMs, as the authors do, then I think one should start the process on the level of 2017 (see reference above) and not on the original level of 2011. The main reason is that in the 2017 version a new DEM is computed (MMASTER) with superior image matching that increases the reliability of the DEMs.

Another comment is related to the ‘master/slave’ concept to co-register DEMs. As is apparent from Table 2, the authors use as a master another ASTER DEM. That makes all computations relative to the master (which is essentially affected by the same systematic sensor errors as the slave) and thus precluding comparisons to an accepted ground reference system. In the area of the test site in Greenland are alternative sources that would be much better suited for serving as a master DEM (e.g. ICESat-2, World View DEMs, ATM airborne laser altimetry).

The research results presented in this paper include a comparison between the methods proposed by Nuth/Kääb and Rosenholm/Torlegard. The results of these comparisons can be found in Table 3. The numbers confirm what other researchers have found. The question I have is the definition of AverageMed which is used throughout the paper. How does it compare with more traditional statistical error measures such as mean, median, standard deviation?  

Another conclusion the authors make is that GAM spline fitting can be used to reduce complex systematic errors that are still present after geo-referencing. These research results are OK but limited to a specific sensor (ASTER, 25 years in space, outdated technology, complex suite of systematic errors that change in time). Moreover, since GAM spline fitting seems to play an important role in this paper I would strongly suggest to cover it in more detail and provide readers with explanations why you choose it.

Though the paper is written well I have doubts that it is suitable for publishing in this journal in its current form.  The methodology presented in this paper should be made more relevant to cryospheric research or might be better suited for a journal that is more focused on new methods and algorithms.