A computationally efficient depression-filling algorithm for digital elevation models, applied to proglacial lake drainage

Berends, Constantijn J.; van de Wal, Roderik S. W.

doi:https://doi.org/10.5194/gmd-9-4451-2016

Articles | Volume 9, issue 12

https://doi.org/10.5194/gmd-9-4451-2016

© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/gmd-9-4451-2016

© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 9, issue 12

Development and technical paper

|

15 Dec 2016

Development and technical paper |

| 15 Dec 2016

A computationally efficient depression-filling algorithm for digital elevation models, applied to proglacial lake drainage

Constantijn J. Berends and Roderik S. W. van de Wal

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Final revised paper (published on 15 Dec 2016)
Supplement to the final revised paper
Preprint (discussion started on 17 May 2016)
Supplement to the preprint

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'Review of Berends and R. S. W. van de Wal submission', Lev Tarasov, 29 Aug 2016
- AC1: 'Author comment replying to the referee comment by L. Tarasov', Tijn Berends, 30 Sep 2016
  - RC3: 'author response concerning computational speed', Lev Tarasov, 30 Sep 2016
RC2: 'Referee Comment', Anonymous Referee #2, 05 Sep 2016
- AC2: 'Author comment replying to the referee comment posted by anonymous referee #2', Tijn Berends, 30 Sep 2016

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Tijn Berends on behalf of the Authors (25 Oct 2016)

ED: Referee Nomination & Report Request started (26 Oct 2016) by Didier Roche

RR by Anonymous Referee #2 (04 Nov 2016)

Suggestions for revision or reasons for rejection

The modifications made by the authors to the Introduction & Methodology are minimal in response to my comments, I do not feel that they have improved the clarity of the paper. I assume the authors believe that all the information is there so they don’t think it needs modification, however, I find these parts of the paper hard to read and think the authors could be much kinder to the reader. I hoped the authors would understand my points and address them, instead I now feel I must detail points more explicitly. I leave it to the Editor to decide whether to ask the authors to have another go at clarifying the paper for the benefit of a non-specialist.

My first point: The introduction does not give enough background to the task, such that I had to read it a number of times to understand exactly what the task at hand was.

In the first line of the introduction, the “problem” of determining drainage routes is introduced, and the introduction then goes on to explain the importance of the location and magnitude of the lake drainage. This is ok (though could still also be improved). However, after this, you need to be more clear about the exact problem you are addressing, why it is a problem, and how you are addressing it, and exactly what the algorithm does. On line 12, the sentence beginning “Doing this” (try and avoid using “this” - reiterate what “this” is) is not clear, and leads to confusion for me over the mask and the filling aspects. Here is my understanding of what you are doing, correct me if I am wrong…
“In order to model the extent and volume of lakes over time, and, hence, where these lakes discharge to the ocean, a land/ocean mask must first be defined. The land/ocean mask delineates ocean areas below sea level that have an open connection to the ocean, using the ice sheet extent and sea level at a given time. Large changes in the land/ocean mask occur, for example, where the ice-sheet at times covers most of the Canadian Arctic Archipelago or blocks the Hudson Strait. Alterations to the mask change the location where spill-over from the lake and drainage events reach the ocean over time. A “flood-fill” algorithm (Zhu et al. 2006) can be used to determine the land/ocean mask with a given sea level, and then subsequently used to fill depressions that are unconnected to the ocean to a given level, or to overflow level. Quantifying the volume of the filled depressions allows the potential volume of the lake to be calculated in order to determine how much melt-water is released into the ocean and where.”

Then the following clarifications:
“When applying commonly used **what sort of** algorithms (Arnold, 2010, Doll and Lehner, 2002, Tarboton et al., 1991, Zhu et al., 2006) to a problem involving such large geographical grids and long time-scales, computation time **for filling depressions?** can become a limiting factor, particularly when the geometry is changing over time and the procedure has to be repeated over many time steps.

In this study, we describe and evaluate several improvements to a standard algorithm for filling depressions in a DEM in order to improve the computational efficiency **for calculating lake volumes**.”

The last two paragraphs are not introduction material – these would be more suited for the methodology section.

My second point: Further there is not much detail on the default algorithm, the reader is left to go and read the paper by Zhu et al. (2006), such that it is a bit hard to follow independently.

I couldn’t see any modification to the description, beyond the addition of a figure, which does not really help to clarify the situation very much. The description of which cells go into the stack is not written very clearly.

What would also help the narrative is a final line stating how you go from delineating a lake to a value for the total volume of the depression, given that (I think) that is what you have said you want to calculate in the introduction. I’m a bit confused as to what you are calculating in the paper (just delineating lakes?), and what you want to calculate in the wider studies (lake volume?).

I also notice that in Figs. 1 and 2 that there are three green shades (and perhaps a 4th, but I think the black looks green to me!) and only two green shades described in the caption which means I find these figures confusing.

My third point: There are also a lot of vague statements such as “A second issue is an efficient way to determine the water level” on page 3, line 22. Because you don’t introduce your terms, such as “base level” and “water level” it is not always easy to follow the methods. Be more specific in these statements to help the reader understand what it is going on. Another example, on page 4, line 18 and Fig. 1, you talk about a true/false mask but don’t define what this is. In Fig. 2 you talk about a land/ocean mask, but all I can see is DEM elevations? Is the deep blue actually a mask and not elevations? In this case, this needs to be in the legend.

Ok, the bit where you had used base level is clearer now, but I think you need to more clearly use and define different terms for the water level – sea level, lake water level and overflow level. Also, technically, how do you identify the overflow level? You use water level for all these terms, so I still find the explanation on p4 difficult to understand.

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ED: Reconsider after major revisions (04 Nov 2016) by Didier Roche

AR by Tijn Berends on behalf of the Authors (22 Nov 2016) Author's response Manuscript

ED: Publish as is (23 Nov 2016) by Didier Roche

AR by Tijn Berends on behalf of the Authors (30 Nov 2016)

Short summary

This paper describes several improvements to the so-called "flood-fill algorithm" – a computer program widely known for its use in the "paint bucket" tool in several drawing programs such as MS Paint. However, it can also be used to determine the extent and depth of lakes in a topography map, which is useful in hydrology and climatology. In such cases, the default algorithm can be too slow to be of much use. Our improvements can make it up to 100 times faster, making it much more feasible.