Summary:

In this manuscript Charrier et al. present TICOI (Temporal Inversion using Combination of Observations and Interpolation) an open-source package in Python for the post-processing of ice-velocity observations derived from satellite observations. This TICOI package uses the principle of temporal closure of velocity measurements and builds on previous work by several of the authors which demonstrated this technique’s application to ice velocity. This manuscript substantially develops this technique by introducing methodological developments to address shortfalls in previous versions, producing an open-source Python package to implement the method, and validating against GNSS glacier motion measurements.

Overall, in my opinion, this is an excellently written manuscript. I found the explanation of the TICOI method to be easy and intuitive to follow with an appropriate level of detail. The presentation of the results is clear, and the performance of the package is impressive, particularly when applied to retrieve sub-annual velocity fluctuations from long temporal baseline measurements. The authors provide a transparent and balanced assessment of the performance of their method, including a comparison to a conventional moving average smoother and using multiple datasets as inputs. I was also pleased to see a thorough discussion of the errors associated with remote-sensing ice velocity measurements, as this is overlooked in many studies.

I am confident that the method and software package described in this manuscript will be of interest to anyone in the Cryosphere community who works with remotely sensed ice velocity datasets. Adoption of this method would improve the velocity products produced in the community, in terms of accuracy and the representation of errors. This has great potential to be valuable to downstream users of these data for applications such as the study of processes influencing ice motion and modelling glacier and ice sheet behaviour.

Additionally, the authors say they will make their TICOI python package available online upon publication of a final manuscript, however, the package is already available at the link provided in the manuscript. Therefore, I took a brief look to assess the quality of the author’s python package at this early stage. Even at this point before publication, the TICOI package is well documented including example code. The authors may choose to develop the presentation and documentation of the package further before publication, but as it stands, I have no concerns about the code and data availability. This is an excellent example of how to present open-source code. I applaud the authors for their effort in this regard.

I have a couple of small general comments regarding how the clarity of figures, terminology, and options for shortening the manuscript. After that, I have given line-by-line comments on more specific points. I hope these will be useful for improving the manuscript. See below:

Overall comments:

Figures: The quality of figures in this manuscript is very high. However, there are a few places where I think small changes would significantly improve the clarity and usability of the figures.

The choice of grids and map projection should be made more consistent. In Figure 2, the plots are given with a lat/lon border grid, but Figures 3 and 6 use an x/y grid. I would recommend maintaining the same coordinate system across these plots for better interpretability. Likewise, the units and map projection for Figure 3 are not given in the caption. I assume it is EPSG:3260 like Figure 6, but this isn’t clear.

It can be hard to read the figures in this paper when they are presenting large volumes of ice velocity data (eg. Figure 3c, Figure 8a, Figure 11). Could these figures be expanded to the full width of a page, or use vertically stacked separate axes for the image-pair velocities and TICOI results? Similarly, the red/pink/orange colour scheme is difficult to read, especially in Figure 8a. I appreciate that presenting this volume data on one plot is always difficult.

Length: The manuscript is somewhat long with 12 figures and 2 tables. Moving some of the figures to the supplementary material could address this and make the paper more focussed on the key results and takeaway messages. Specifically, I would suggest figures 5, 7, 10 and 12.

Use of the term ‘regularized’: The term ‘regularized’ is used early on (line 58) here to refer to an even temporal sampling, but later in the manuscript is used for regularization in the context of solving an ill-posed problem. The latter usage is what I would expect the term to refer to in a scientific paper, and I think most readers would approach it this way, too. I think it’s okay to use regularized to refer to even temporal sampling where it is clearly explained, like it is with the brackets in line 58. However, in some places in the manuscript it is ambiguous, for example ‘regularized’ and ‘regularization’ in the title and abstract could refer to either aspect. For the sake of clarity, the authors could consider choosing a different term to refer to sampling the data on a regular time-step. For example, something like ‘temporal standardization’. Although I concede this is not as catchy.

Line-by-line comments:

135: There is a hard limit of u =10 for iterations. Can you comment on how often this limit is reached? What is the average number of iterations required?

156: Could you also comment here on how this RMSE convergence behaves for faster glacier flow, e.g. the > 1000 m/yr speeds that are common for outlet glaciers?

206: Can you comment on how the VVC metric is affected by changes in ice flow direction? This can be significant on ice-shelves particularly around rifts.

231: Should be ‘validated’ not ‘validates’

293: In this section, it would be insightful if you were able comment on how the different algorithms perform, ie what are their strengths and weaknesses? They are quite different, so this may be helpful to a reader who is not familiar with these datasets.

347: I don’t think that Figure 3a supports the statement that ‘Over stable areas, the difference has median values of 0.0 m/yr’. In Figure 3a it appears that most of the areas outside the glacier outlines have a negative value, as shown by the general blue shading. Can you explain this difference and clarify this point in the manuscript?

Figure 3 caption: The caption refers to white lines for glacier outlines, but they are grey in the figure.

Figure 3 caption: From the figure and caption it’s not obvious to me if the difference being plotted is TICO – TICOI_detect_temp or TICOI_detect_temp – TICOI. Based on Figure 3c I think it’s the latter, because this value is positive and point A is red on the map, but it’s not clear to me. This should be clarified in the caption.

369: In this paragraph including some absolute values as well as % change could be useful for giving the reader a better understanding of the results.

370: It’s confusing to say KGE increased if the range includes a negative percentage.

371: In my opinion it is best if the term ‘significant’ is reserved to refer to specifically to statistical significance. I would consider choosing a different term where possible, also on lines 387 and 445.

Figure 9 caption: The caption refers to a logarithmic scale in a), but the colourbar isn’t logarithmic.  

477: I think this should read ‘RMSE even slightly increases’?

Please see the attached pdf for the full review.

Here is an overview:

The authors describe a new open source python package, TICOI, for the creation of regularly temporally spaced velocity measurements from large velocity pair stacks. The package builds on some of the authors recent work with ‘overdetermined system’ inversions, and adds an interpolation step to create regularly spaced outputs in time. The manuscript is well written overall, and the package described will be useful to the community. I have included a number of comments below, but these are all relatively minor and should not require any major reorganisation of the manuscript. Overall, I recommend publication in TC following minor revisions.

On the whole, this will be a substantial improvement to our treatment of ice velocity timeseries, and to their usability by wider audiences (the uneven temporal spacing is always a source of confusion). There are still a number of open questions about the best way to treat uncertainties in this data but I cannot fault the authors for not resolving these here. This package also makes for an excellent baseline for future development to build off, particularly as the authors have made sure it is open source and adequately documented.