Review of “The damability function: A probabilistic approach to regional landslide dam susceptibility analysis applied to the Oregon Coast Range, USA” submitted by Paul M. Morgan and colleagues (egusphere-2025-580)

Dear Authors,

In this study you are concerned with estimating how likely it is to have a river dammed by a landslide in the Oregon Coast Range, United States. You draw on data of nearly 20,000 previously mapped landslides and several hundreds of landslide dams, and present a logistic regression that outputs the probability of recovering a (known) landslide dam as the target variable. You consider landslide volume and valley width as predictors and thus obtain a quantitative estimate that you term “damability”. You find that the potential for damming is likely higher in steeper headwaters than in larger rivers with wider valleys. You cast your results in several maps and also estimate the water volumes likely to be impounded in damming scenarios. This type of probabilistic treatment is long overdue, and I am happy to see that you tackled it.

Overall, your study surely fits the scope of the journal and may well be of interest to both scientists and practitioners dealing with landslides, rivers, or mountain hazards in general. You present your study well, albeit in a bit longish format that could benefit from some shortening (without losing any information). I would like to see this published eventually, but I also believe that you may need to consider a number of items beforehand:

--- General Comments ---

The abstract is easy to understand, but could also reveal some more details or benefits concerning the predictions from your damability function.

The introduction (section 1) could explore a bit more any previous work that tried to figure out where landslide dams occur most likely. Consider reviewing in more detail some attempts at prediction. You might also want to summarize briefly what the many inventory studies tell us about the relative catchment position of landslide dams.

The outline of the study area (section 2) is a bit short and may benefit from some more pointers to studies that readers can chase up. The landslide (dam) inventories do need more detail here, though, as the form part of your training data set. Please provide some more background and insights from these inventories.

The methods section (3) could also be a bit more revealing, especially about the landslide data and their constraints:

• What is the estimated error on the landslide volumes and were they all derived consistently? A potentially confounding issue is that you use two independent, and differing data sets. One has a couple of hundred landslide dams, whereas the other features more than 19,000 landslides. This choice may undermine some assumptions of likelihood-based model fits.

• Your general damability model (Equation 1) has an awkward specification, and uses the ratio of landslide volume to valley width, whereas you implicitly made the case in Fig. 3b/c that both these should be independent. Equation 1, however, specifies a regression that solely models the interaction effects between landslide volume and the inverse of valley width (plus an estimated off-set), hence some metric of “valley narrowness”. Maybe emphasize your reasoning behind this more candidly.

• Despite reading and trying to reproduce this section several times, I found it confusing, partly because (i) log-transformations occurred without consistent mention; (ii) the landslide volumetric distribution is included in a model designed to predict damming (instead of volumes); (iii) the model parameters eluded any description or interpretation. Why not simply use a logistic regression with landslide volume and valley width as additive predictors? This would be compatible with what you show in Figs. 3 and 7, while keeping the three fitting parameters, though in a much more accessible way (i.e. as marginal effects of landslide volume and valley width, if properly standardized).

• For some reason, I could not arrive at some of your parameter estimates; perhaps I must have mistyped or overlooked some critical information (see below). Nonetheless, please describe your model setup as clear and rigorous as possible, so that your readers can reproduce it. Section 3.3.2 seems like a candidate section to drop entirely. If you decide to keep it, you should describe the underlying models in due detail.

The results section (4) may also need some attention.

• The derivation of Equation (3) could be more explicit, the parameter estimates re-checked, and their errors propagated.

• In Equation 4 you express damability as a function of valley width alone, as opposed to Equation 3, where you used the ratio of landslide volume over valley width. The simpler Equation 4 ignores the uncertainties of the log-normal fit to the landslide volumes: you boil down the number of parameters at seemingly no cost. You could argue equally well that the distribution of valley widths matters also, but you bring this up in the model validation later on. Please be consistent.

• Again, I am puzzled why you discarded the logistic regression with landslide volume and valley width as additive predictors, thus implicitly accounting for the distributions in both (with their interaction arising naturally from the log10-transform). You could then still use the “SLIDO PDF” in Fig. 7 (and the distribution of valley widths in your study area) to estimate predictions.

• In this context, you might want to explain why the decision boundary in Fig. 7 becomes more precise with smaller landslides and narrower valleys: the transition between high and low damability estimates is more stepped for this configuration than for larger landslides in wider valleys. This model outcome is counterintuitive as your “SLIDO PDF” shows that your data density is quite low in this case. The decision boundary should be most distinct where data density is highest.

• The part about estimating model performance (Fig. 8) brings in information more relevant to the methods (such as sample size, balance/imbalance), and again raises points better suited to the discussion.

The discussion (section 5) could be slimmer and more to the point.

• Besides trimming several wordy or overly repetitive statements, I suggest you transfer some major chunks of text to the study area and methods sections to fill in some of the gaps there (see specific suggestions below).

• Another obvious asset would be to discuss in more detail the model performance and alternative formulations. For example, what other extensions to your model could you think of other than adding more predictors? You duly mention that only a fraction (of the order of a few percent) of the known landslides formed dams. In terms of logistic regression, this can be a problem, as the method assumes data that are roughly balanced across both classes (dam/no-dam). You can sample the larger data set as you did, but need to demonstrate that this sample is representative. Bootstrapping is one possible method, while rare-event logistic regression is another.

• Why not use landslide runout instead of volume? Some aspects regarding your data might also need reflection: how many of the SLIDO landslides were catastrophic, how many were (or are) slow-moving such that, even if they have a large volume, they might not necessarily warrant river damming?

The conclusions give a good summary, but could feature some more quantitative detail. I am not fully sure whether all your statements here are fully supported by the data, though (see below).

--- Specific Suggestions ---

5: Typo in “alex”.

15: “landslide dam formation susceptibility” – Please avoid four nouns in a row.

20: “represented as” → “estimated from”.

20: “verify” is rather “validate”?

22: “correlates” → “correlate”?

24: How do you define “large lakes” and “low drainage areas”.

25: “widespread susceptibility” – Sounds a bit vague. Do you rank this susceptibility somehow by potential landslide or lake volume?

26: “this hazard should be considered in the Pacific Northwest” – Reads as if this hazard is unknown there as yet. Consider rephrasing.

43: “anywhere with steep slopes” – Steepness helps, but landslides can also occur in marginally inclined terrain.

51: “are potential hazards anywhere steep slopes abut rivers” – Check grammar.

58: Delete “both”.

73: “for situations where the properties of a future landslide must be inferred” – Contradicts what you state in the following “inferred from only two parameters: landslide volume and valley width” (l. 75). So is landslide volume assumed or inferred? Might pay off to define this index here.

78: “will” → “are likely to”.

78: Delete “or dam non-formation”; this is the default situation.

79: Similarly, delete “formation volume and non-formation volume”.

80: “satisfactorily” – Sounds a bit vague. You might want to discuss the reliability of this approach.

90: “compound” – Is this the term you want to use? Maybe the grammar needs a check here.

92: “by implementing a workflow based on” – Wordy; simply replace by “from”?

94: “large database of mapped landslide deposits” – From the Oregon Coast Range?

94: “define” → “fit”.

95: Delete “empirical”: this is what “fit” says.

98: “found” → “estimated”.

98: “damability” – Why use quotation marks here. You had already used this term in the text.

100: See previous comment.

100: “are therefore useful” – Does not follow logically, and the usefulness remains to tested.

104-112: This part reads like a mini-abstract. I think you can safely delete this.

109: “dangerously large lakes” – The literature on landslide dams indicates that not all large lakes are dangerous.

110: Delete “investigate and”.

120: Which part of the landslide dam do the yellow dots refer to? One yellow data sits some 70 m beside the channel in Fig. 1c.

128: Delete either “annual” or “per year”, and specify whether this an average rainfall. I think you can also safely delete “(65-200 in.)”.

141-154: While I think this navigation aid has some merit, it also takes up some space. You explain all of these steps in detail below anyway. Consider trimming.

149: “damability function (DamabilityOCR)” – Please consider a shorter abbreviation. Perhaps consider including what the function depends on.

150: “the function (DamabilityOCR-v)” – How does this differ from the function in l. 149?

155: What is a “non-dam inventory”?

157: “SLIDO landslide inventory records mapped landslide deposit polygons” – How many landslides are in this inventory?

160: “characterize” → “estimate”.

170: Please explain the two types of nodes connecting the solid lines.

175: What do you mean by “flow path uncertainties of river valleys”?

178: “‘annual constriction ratio’, ‘Dimensionless Morpho-Invasion Index’, and ‘Dimensionless Constriction Index’” – Please provide the appropriate references directly, so that readers can chase these up. A brief explanation of these indices can help a lot here.

182: “global scale landslide dam formation susceptibility evaluation” is a wieldy term. Again, please briefly describe this method. This is really something for the introductory section (see general comment).

184: “sufficiently small drainage areas to capture and calibrate with landslide dams in the OCR” – This is a point that you have not demonstrated yet.

188: “large historical dataset” – Compiling cases from?

189: “manually placed” – Without any further constraints?

194: Delete comma.

194: “can make analysis of landslide dam likelihoods difficult” – Unclear. Is the method not designed to make this analysis easier?

195: “non-formation volumes” – This keeps popping up and reads as if volumes are dependent on the formation of dams. Consider rephrasing (or simply omitting) throughout.

196: “does not provide any additional uncertainty values other than a domain position” – Well, it does. You can easily estimate the misclassification from Fig. 3b by counting the false positives and false negatives, etc.

198: “uncertainty in domain position” or “uncertainty at the domain position”? There is a difference between the two. Ideally, you want to estimate both together.

189: “identify the damability function position and uncertainties” – See previous comment. What do you mean by position? The output of a logistic regression is a probability of success (or class membership).

201: How do you define “river stretch”?

209: “at every point where a valley width measurement is made” – See previous comment. This seems to be related.

217: “dam-not-formed slides” – Style. Similarly, you could relabel “Dam Non-Formation Domain” to “No landslide dams formed” in Fig. 3b. Note that regression equations in Fig. 3b formally need units of the intercept; these units depend on the differing exponents.

218: “defined by lack of dam-formed slides below it” – Well, several red dots lie below this line.

Fig. 3c needs more explanation in the caption. Why do you show so few landslides from the SLIDO data if they contain more than 19,000 landslides? How did you come up with the four classes A-D?

233: “than restriction to a GIS program” – Unclear, please elaborate.

234: “the ease of use in comparison to Python based codes available” – Difficult to tell because you did not demonstrate this yet.

241: “capturing the prominent drainage area positions of the mapped landslide dams in the study area” – See general comments. So far, you have disclosed very little about landslide dams in the study area.

244: Why choose a “threshold elevation (10 m)”?

250: “river meanders don’t create their own valley walls” – Needs an explanation.

265: What is the color scale along the river in Fig. 4d.

268: “size of future landslides can be estimated numerically based on physical laws” – Which physical laws do you mean?

277: “log-normal functions can fit landslide size inventories” – You mean log-normal “probability densities” or “probability distributions”. You can fit any model: the question is how well it fits.

278: “capture absolute characteristic landslide sizes, while power laws only capture relative frequencies” – I do not follow. What do you mean by “absolute … sizes”?

280: “advantageous for working with statistical models” – Explain why. I think in the way that you refer to log-normal “functions” here makes them statistical models already.

284: “defined” → “with”.

284: “defined by a mean (𝜇) of 4.44” – What are the units of this mean?

285: “standard deviation (σ) of 1.25 (or ~28,000 m³ plus or minus one standard deviation)” – Note that the standard deviation cannot be symmetric in volume. You seem to refer to the log-transformed volumes here.

286: “by the mapper” – How is the mapper? Was that you or the SLIDO team?

287: “estimates or measures the slide depth and multiplies that by the slide area” – How do you estimate individual slide depths for >19,000 landslides?

291: Where is the y-axis scale for the “log-normal fit”? Please also report the fitting method as well as the goodness of fit.

295: “Spatially variable estimation of landslide volume (not implemented in final workflow)” – Consider dropping if this section is irrelevant to your final results.

299: “feedback into the valley widths” – Unclear.

307: “relatively effective” – Relative to? Effective in what way?

308: “consider if such relationships hold for the OCR” – Does SLIDO consist only of earthquake-triggered landslides? That would be a prerequisite for comparison, right?

309: “The parameters we used” need some justification. Why are these most relevant for predicting landslide volumes?

313: “500 m radius moving window” – Please explain this choice.

316/17: “general” → “generalized”.

316: “linear and quadratic n=4 functions for each predictor variable” – Needs an explanation.

322: “bi-logarithmic slide volume/valley width parameter space” – In the context of logistic regression, you would refer to this as the predictor or input space. The parameters describe the model instead of the data.

327: “parameter space” – This is technically incorrect. See previous comment.

328: “largest surface area” – Why not volume?

329: “Signs of past dam formation” – Refer to some key sources in the literature to support your assessment here.

338: “converted the area to volume using the area-volume scaling relationship” – This is slightly confusing. Did you not take the volumes from SLIDO data directly (l. 285)?

351: Please specify units for landslide volumes and valley widths in Equation 1. Please also report the corresponding units and definition ranges for parameters k, X0, and a. You should also note the (somewhat awkward) constraint that aW_v must be unequal to 1. Dropping the base 10 is probably easier to read without changing the result.

353: “reflecting the likelihood that a given combination of landslide volume and valley width would form a landslide dam” – Equation 1 shows no probabilistic statement in this regard. Please elaborate.

354: “damability function was fit using nonlinear least squares regression” – The sigmoidal function of a logistic regression prohibits the use of least squares. Equation 1 has results limited to the unit interval, so least squares become increasingly limited and meaningless towards the bounds of this interval.

367: “test landslides in Burns et al. (2016)” – This is unclear. Please explain.

368: Insert “here” after “defined”.

377: “Although these relationships were developed using alpine river geometries, they are likely still a good precursory estimate” – Avoid biasing your readers with these speculations. Why not show some results first.

383: “18,000” – l. 160 states “19,000”.

384: “dataset is well represented by a lognormal statistical distribution” – Hard to tell, especially in the center where the data could also be bimodal. In any case, please provide a measure of fit. You can delete “statistical” here.

385: Delete “single lognormal”.

387: “This statistical distribution is inserted directly into the damability function described in section 4.2”. Repetition. Consider deleting.

388-396: See previous comments about possibly deleting, or at least trimming, this content together with Fig. 6 and Table 1 (which is not very informative anyway).

419: Please provide the fitting errors for all model parameters. It may pay off to explain what these parameters mean here. Does landslide volume or valley width have a greater affect on making a location prone to damming? See my general comment on reformulating Equation 1.

420: You seem to mix the terms “probability” and “likelihood” freely here, although they are not the same.

423: Delete “deterministically” – Your inference is based on a statistical model.

423: “landslide dam formation or non-formation volume” → “the minimum landslide volume needed to dam a given valley width”?

429: Please explain how you arrived at this result. I assume you set the exponent in Equation 2 to zero. For some reason, however, I failed to achieve this if plugging Equation 3 into Equation 2. For example, if I assume a 1000-m wide valley, Equation 3 predicts that the minimum volume for damming is 0.004 * 1000 ^ 3.861, i.e. about 1.5 billion, cubic meters, which is consistent with what Fig. 7 shows (although the exponent there is 3.859 as opposed to 3.861 in Equation 3). Yet, if I plug this into the exponent of Equation 2: 2.5937 * (log10(0.004 * 1000 ^ 3.861) / log10(2.338 * 1000) - 4.0168), I obtain ca. -3.35, whereas the result should be zero for a damability of 0.5. Please also make sure to carry over the regression estimates to Equation 3.

433: “we compute damability, combining uncertainty in the damability function and range of expected landslide volumes resulting in Eq. 4” – Unclear how you computed this. Please elaborate.

435: Equation 4 really refers to log10 of valley width, right?

436: “Equation 4 (DamabilityOCR-V) includes both the logistic regression fit to the local landslide

dam/non-dam inventory, and the lognormal volume distribution of local landslide dams.” - Why introduce the “1 minus” term in Equation 4? Aim for consistency with your probabilistic interpretation of Equation 3.

439: “Damability values computed using Eq. 4, range from zero to one, and reflect the probability a

landslide forms a dam in a valley of a certain width” – See previous comment.

441: “uncertainty in the damability function” – Where is this included? Essentially, you subsume this in the parameter estimates.

445: The “SLIDO PDF” in Fig. 7 is not a PDF, at least not judging from the x-axis units. It might be good to mention the error estimates of the damability in the discussion.

453: “verification” → “validation”. Please keep results and interpretation separate. Save this point for later.

454: “randomly withheld 12.5% of the dam forming points” – Why 12.5% only? “points” should be “landslides”.

458: “does not deviate much from the fit” – I think you can be a bit more quantitative about this.

464: “ROC curves compare positive results (river points with a dam) and negative results (river points without a dam).” – ROC curves relate relative fractions of positive and negative predictions to various decision boundaries.

465: “we do not have many mapped river stretches without dams so we substituted the entire population as “negative results” – You may want to mention all this info much earlier. Make sure you make clear whether your classification or whether your validation is potentially biased by imbalanced samples.

479: “Across the study area, 51% of the calculated damability values” – It would be nice to have a figure relating the distributions of damability vs. valley width or percent of river length. Something like that could make a nice summary of your model predictions.

500: Consider more contrast for the landslide-dam symbols in Fig. 9.

512: The color scale in Fig. 10 tends to smooth out the order-of-magnitude variations in lake volumes.

524: “and uncertain domains” – Unsure what you mean here.

525: “allows for a better characterization of the uncertainty of dam formation” – In more formal terms, your model allows a probabilistic estimate of how well you can recover mapped landslide dams from a combination of predictors.

527: “makes adding other useful metrics (i.e., landslide susceptibility, or estimated dam lake volume) more straightforward” – How do you “add” these metrics?

529: “simplifies hazard visualizations” – To be fair, Fig. 7 does not look much different from Fig. 3b in is setup.

530: “damability function regression methodology” – Bulky term. Why not simply use “logistic regression”.

533: “we have the best fit currently available” – By design, any regression model will generate the best fit.

535: “underrepresented valley widths or volumes, could alter the shape of the function” – Well, they should, though this is something I cannot see for the combination of small landslides and narrow valleys (see general comments).

536: “form of the damability function represents how efficient a slide of specific volume is at running out” – Really? Which model parameter tells you that?

539: “Pollock (2020)” – Is this PhD thesis publicly available?

541: “coefficient of 0.0018” – Needs units.

543: “landslides of a given volume have a consistently larger runout length than the width of the valley that they can dam” – In your study area?

545: “fact” → “observation”.

551: “has a lower Y intercept suggesting small slides can dam larger valley widths” – There is no y-intercept in log-log space. Do you refer to unit landslide volume and valley width here?

554: “speculate that small slides in Oregon may be dominated by long runout debris flows” – Difficult to assess for your readers without any background on lanslides in your study area. Something for the wish list for section 2.

547: “data gaps and outliers in the calibration slides” – Vague. Can you give some examples?

547: “Local geology, geomorphology, and climate all likely control the form of the damability function” – By design, they do not. You only consider landslide volume and valley width as possible controls. What you refer to is the misfit between model and data.

575: “underestimating the damability for the wide valleys because they may be more likely to experience a large volume landslide” – But these large landslides may be commensurately rarer (Figs. 5, 7).

590: “The SLIDO inventory includes a wide range of failure styles, includes landslides which occurred at different times by different triggers on adjacent slopes, and was mapped by several different authors.” – Again, this information is likely more useful further up in the text when you describe your methods. Like before, I suggest dropping this part from the study.

596: “makes estimating the volume of a possible future landslide on any given slope difficult” – See previous comment.

598: What are “hyper local properties”?

599: Delete “In reality, ”.

602: “earthquake triggered landslide sizes (only maximum area per slope unit) may be exceptional when it comes to landslide size predictions” – Why should they be exceptional? This notion mixes issues of data quality, method of analysis, and possible physical controls. Can you separate out the latter with confidence.

604: “not straightforward to use hillslope properties or geometry as a proxy for landslide volume in landslide dam susceptibility analyses” – And yet you do so by using valley width as a proxy.

607: “the largest possible landslides a hillside could produce, which may be the most important factor for landslide dam analyses” – Avoid undermining your results. If landslide volume is most important, what role then plays valley width? Using the two as additive (and standardized) predictors in a logistic regression will give your their relative weights in terms of damability.

612: “Instead of proxies, or a local regression model, we are forced to use a region wide empirical approach to landslide volume estimation based on the mapped landslides within the study area” – I am not sure that I follow. Please elaborate.

618: “make this less applicable” – This refers to “inventory”?

621: “susceptibility estimates dominated by valley width” – Refer to the appropriate Equation here; “dominated” is probably to exclusive, because you chose this predictor yourselves.

627: Section 5.1.3 is probably better suited for the end of the discussion.

634: “While the methodology of the landslide mapper may vary between studies, because this method only uses the inventory to define a lognormal volume distribution it is insulated from variations in inventory quality and completeness.” – Not sure what you want to say here.

652: “small effect on spatial trends” – Trends of what?

654-665: Reads like a great motivation for valley width as a predictor in your damability model. Why not use this earlier up, either in the introduction or methods part?

666-683: Similarly, much of this paragraph contains much needed detail for the study area description. Consider shifting this up.

Fig. 11: Why not highlight the “trends” that you show here? Panel (a) has incorrect unit for drainage area.

694: “high relief areas in the south of the study area do not always correlate with a separate rock type” – Not fully clear. What you mean by “separate”? How can you correlate relief as a quantitative measure with rock type as a categorical variable?

700: “In the Himalaya” – Feels a bit out of place given that you discuss the OCR in the preceding and subsequent sentences.

707: “Volcanic rocks may host narrower rivers” – The discussion about lithological controls (starting l. 690) is difficult to appreciate with the sparse information you provided in the study area. Again, I recommend delegating some material from here to that section.

714: “study area 4.6 to 4.4 respectively” – Check grammar. What are the units? Consider adding a formal test for difference in these means.

719: “do not show a decrease in landslide susceptibility in regions of volcanic rocks” – Assuming these models are accurate, of course.

761: “lake volumes of 1 million cubic meters are the minimum recorded lake volumes for catastrophic outburst floods” – How reliable do you think this estimate is?

766: “Landslide dam disasters are usually triggered by exceptionally large landslides” – Avoid the pitfall of relying too much on reviews that are over three decades old.

Fig. 13: Please show entire distributions and avoid truncation of the 95th percentile landslides. You show five colors but only two y-axes. Try to make it clearer that points refer to counts. The curves cannot all be PDFs, by the way. If they were scaled properly, you could make statements about the different likelihoods for each of the scenarios you discuss here.

802: “Future work” – You already discussed this earlier. Consider shortening.

813: “not always predictable based on local geomorphic and geologic factors” – Not sure if this statement is fully supported by what you show: here you refer to the data, but not the choice or suitability of the models you chose.

815: “can be successfully used to assess landslide dam susceptibility” – Summarize how successfully.

818: “visualize landslide dam formation likelihoods” – Refer to figure(s) showing this likelihood.

This study presents a regional-scale workflow for mapping landslide dam formation susceptibility by integrating river valley width and landslide volume—an interesting and critical contribution to the field. The proposed damability function offers new and transferable knowledge of value to both scientific and engineering communities. The manuscript is well-structured and clearly written. I recommend minor revisions before publication in NHESS.

Specific Comments:

1. The authors suggest the workflow is broadly applicable to other regions. It would be valuable to discuss its potential application in highly dynamic settings such as the Tibetan Mountains, where mega-scale landslide dams and outburst floods occur frequently (e.g., Zhang et al., 2024, Nature Communications, 15: 2878). In such contexts, factors like significant erosion may influence dam stability. Could the method be extended to incorporate these processes?
2. Machine learning is increasingly used in large-scale hazard assessments. Please briefly discuss whether AI could be integrated into this workflow in the future, including potential benefits and limitations.