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Influence of river incision on landslides triggered in Nepal by the Gorkha earthquake: Results from a pixel-based susceptibility model using inlabru

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Elevated river-channel steepness is strongly tied to where the 2015 Gorkha earthquake triggered landslides, but not to how large those landslides were.

desk verdict The ksn-location association is plausible but not identified: the covariate-only design omits spatial random effects and standard DEM covariates, and the paper's own Section 4.3.4 admits the consequence. read the letter →

arxiv 2507.08742 v1 pith:HD5WB2WU submitted 2025-07-11 stat.AP

Man Ho Suen , Mark Naylor , Simon Mudd , Finn Lindgren This is my paper · ORCID
classification stat.AP MSC 62P1262M3062F15
keywords earthquake-inducedlandslidesGorkhaearthquake2015channelsteepnessindexksnlandslidesusceptibilitymodellingspatialpointprocessinlabru/INLAspatiallymisaligneddataproperscoringrules
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper seeks to establish that the normalized channel steepness index ($k_{sn}$), a river-network metric that proxies how actively streams are incising the landscape, is a physically meaningful covariate for earthquake-induced landslide susceptibility. Using the 2015 Gorkha earthquake in Nepal as the test bed, the authors build pixel-based Bayesian spatial point process models of landslide centroids plus separate Gaussian models of log-transformed landslide area, linking them through inlabru's mesh-based disaggregation to overcome misalignment between pixel covariates and point observations. The central result is that elevated $k_{sn}$ is strongly associated with a higher probability of landslide initiation, while landslide magnitude is instead associated with flow distance to the channel. A sympathetic reader would care because the framework deliberately excludes spatial random effects, aiming for a covariate-only model that could transfer to other earthquakes in complex terrain where only DEMs and shaking maps are available.

What carries the argument

The load-bearing object is the normalized channel steepness index $k_{sn}$, derived from the stream-power incision law $S = k_{sn} A^{-\theta}$, which expresses local channel slope as a function of drainage area and thereby isolates the steepness that reflects erosion and incision processes. Around it the paper assembles: (i) a Poisson point process for landslide centroids with intensity modelled in log space; (ii) a Gaussian model for log-transformed landslide area; (iii) DEM-derived distance metrics (relief and flow distance to channel) computed with LSDTopoTools; and (iv) inlabru's mesh-based disaggregation, which resolves spatial misalignment between raster covariates and point observations by projecting both onto a common triangular mesh. The deliberate exclusion of spatially structured random effects (Matérn SPDE fields) is itself part of the machinery: the authors argue that including such fields would inflate posterior uncertainty, bias fixed effects through spatial confounding, and undermine the stated goal of transferring fitted covariate relationships to unseen regions. Model comparison runs on four cross-validation splits (two random thinnings and two 3 km by 3 km checkerboard grids) scored with strictly proper scoring rules, primarily the logarithmic score and the continuous ranked probability score.

What would settle it

Re-run the best-fitting model with $k_{sn}$ recomputed at concavities 0.4 and 0.6 and without the manual hanging-valley substitutions; if the $k_{sn}$ credible interval shifts to include zero or flips sign under any of these recomputations, the claimed link between channel steepness and landslide susceptibility is not robust. As a second check, apply the fitted covariate-only model to a different earthquake's landslide inventory and compare its out-of-region predictive scores with those of a version that includes an explicit spatial random field: if the spatial-field version wins out-of-region, the transferability premise fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that the normalized channel steepness index $k_{sn}$ — the steepness of a river channel normalized by drainage area under a stream-power incision law with concavity fixed at 0.5 — carries a strong and distinct signal for where earthquake-induced landslides initiate, and no signal for how large they become. In a six-model comparison for the Gorkha earthquake, the centroid model (fit6a) combining a smoothed $k_{sn}$ effect, peak ground acceleration, an exponentially decaying flow-distance-to-channel term, land cover, and geology scores best under strictly proper scoring rules (CRPS and RMSE), and the posterior shows elevated $k_{sn}$ clearly increasing susceptibility above roughly $\log k_{sn} = 2.5$, with a flattening plateau at the steepest end. For landslide magnitude, models with $k_{sn}$ are outperformed by fit6b, which uses flow distance to the channel: the longer the flow path to the channel, the larger the landslide. The paper interprets this as $k_{sn}$ modulating triggering probability while flow distance governs failure volume, and it frames the whole approach — pixel-based covariates instead of slope-unit aggregation, and no spatial random field — as a deliberately transferable alternative to existing INLA-based landslide models built on slope-unit polygons.

Load-bearing premise

The model's transferability premise is that its five covariates — PGA, $k_{sn}$, flow distance to channel, land cover, and geology — leave no spatially structured control unmodelled, so dropping the spatial random field cannot bias the covariate effects; that premise is tested only by a checkerboard split inside the Gorkha region rather than against an external region, and it also depends on the manually substituted $k_{sn}$ values in glacial hanging valleys being accurate.

Editorial extensions

If this is right

  • Earthquake response susceptibility maps can be produced from DEM and shaking data alone: channel steepness does the geomorphic work that slope-unit geometry previously did, so no per-region parameterization of slope units is needed.
  • Hazard assessments should separate location from magnitude, because where landslides start is governed by fluvial incision intensity ($k_{sn}$) while how large they grow tracks flow distance to the channel.
  • The covariate-only design means the fitted relationships can in principle be retrained for any mountain region with a DEM, a channel network, a land-cover map, and a PGA raster, without waiting for a new landslide inventory.
  • Traditional DEM covariates that are nonlinear and mutually correlated (slope, elevation, curvature) can be replaced by a smaller set of process-based metrics such as $k_{sn}$ and flow distance, simplifying models and improving interpretability.
  • Per-grid-cell strictly proper scoring rules expose where a model fails locally, such as monsoon-preconditioned slopes, a diagnostic that aggregated mean scores like WAIC or DIC would conceal.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the decoupling of initiation control ($k_{sn}$) from size control (flow distance) points to two distinct physical mechanisms — fluvial incision setting a triggering threshold on adjacent hillslopes, while runout and contributing flow path set volume — which implies that risk planning needs two separate map products, occurrence probability and expected size.
  • Editorial inference: the paper validates transferability only inside the Gorkha region; the natural next test is to refit on one earthquake and score on another (for example, a different large mountain earthquake with a mapped inventory), which would directly quantify how much of the covariate relationship is universal rather than regional.
  • Editorial inference: the unexplained bump in the smoothed PGA effect near 0.42 g is the paper's own hint that residual spatial structure may have leaked into the covariate curves; re-running with an orthogonalized spatial effect would test whether the $k_{sn}$ coefficient is inflated by unmeasured spatial processes.
  • Editorial inference: because the response uses landslide centroids rather than crowns or full polygons, the $k_{sn}$–susceptibility association could partly reflect where centroids fall inside mapped polygons; re-estimating with crown-based points would check whether the association is an artifact of centroid placement.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. Suen et al. present a pixel-based Bayesian spatial model for earthquake-induced landslides triggered by the 2015 Gorkha earthquake in Nepal. Landslide centroids are modelled as a Poisson point process and log-transformed landslide areas as a Gaussian mark, with fixed covariates including peak ground acceleration (PGA), the normalised channel steepness index (k_sn), relief and flow distance to channels, land cover, and geology. The models are fitted with the inlabru framework to handle spatial misalignment between raster covariates and point observations. The authors deliberately omit spatial random effects to favour transferability, compare six model pairs via proper scoring rules under thinning and grid-based cross-validation, and conclude that elevated k_sn is strongly associated with increased landslide susceptibility but not with landslide magnitude. They also include a concavity sensitivity analysis and uncertainty maps for the best-fitting models.

Significance. The paper's strengths are methodological: it applies strictly proper scoring rules (LS and CRPS) with both thinning and grid-based cross-validation, uses inlabru for coherent mesh-based disaggregation of misaligned data, and is transparent about many limitations. If the k_sn association is real, the framework would be a useful, transferable alternative to slope-unit-based INLA landslide models, and the distinction between controls on landslide location and size would be a valuable geomorphic finding. However, the central claim is not yet fully identified: the covariate-only model omits standard DEM covariates that are correlated with k_sn because both are derived from the same DEM, the size-model conclusion is based on removing k_sn from the final model rather than testing it directly, and the manual k_sn filling in hanging valleys is not subjected to sensitivity analysis. These issues are fixable and do not undermine the value of the modelling framework itself.

major comments (4)
  1. [Section 3.3, Eq. (3) and Section 4.3.4] The linear predictor in Eq. (3) contains only fixed covariates, and Section 4.3.4 explicitly acknowledges that without a spatial random field, spatially structured variability may be absorbed by covariates and produce spurious or overfitted patterns. This is a direct threat to the central k_sn claim because k_sn is derived from the same DEM as slope, aspect, curvature, TWI, and distance to streams (Section 2.2.1, Table 1), and the positive rw2(log k_sn) effect in Figure 13a may be an artefact of an omitted topographic control. The grid-based cross-validation in Section 3.4 cannot detect this bias, since a spatially structured omitted variable would still improve within-region interpolation. Please add a robustness model that includes standard DEM covariates or a spatial random effect, or validate on an external holdout region, and report how the k_sn effect changes.
  2. [Section 3.3, Table 3 and Table 6] The claim that k_sn is not associated with landslide size is not directly tested. In Section 3.3, k_sn is removed from fit5b and fit6b because 'initial findings indicated that its inclusion did not enhance predictive performance for landslide size', but no model is reported that includes k_sn together with Fd2Ch or Rf2Ch, and the score differences among size models in Table 6 are very small (for example, LS 2.4616 vs 2.4620 for fit6b vs fit5b in Thinning Set A). The second half of the abstract therefore needs a direct comparison, ideally with posterior intervals for the k_sn coefficient in a size model that also includes the distance-to-channel covariate.
  3. [Section 2.2.2 and Appendix B.1] The manual replacement of k_sn values in hanging valleys with values from nearby geomorphologically similar regions is a subjective step without sensitivity analysis. Section 2.2.2 itself states that the standard algorithm systematically misestimates local k_sn in these areas, so the estimated rw2(log k_sn) effect in Figure 13a could depend on the filling rule. Please report a sensitivity analysis (for example, excluding glacial pixels, varying the substitution neighbourhood, or treating k_sn as missing in those areas) to show that the association is not an artefact of the manual filling.
  4. [Section 2.3] The exclusion of the Siwalik Group, Gangetic Plain, and Sub-Himalayan regions (Section 2.3) is justified by numerical stability, but it restricts the study domain to the high-relief Himalaya. The paper's transferability claim (Section 3.3 and Abstract) should therefore be qualified as applying to similar mountain terrain, and a sensitivity test of the exclusion boundary would help establish how much the results depend on this subjective choice.
minor comments (6)
  1. [Table 3] The row entries for fit5b and fit6b are ambiguous; please clarify which covariates enter each model, in particular whether PGA is included in the size models.
  2. [Section 3.4.1] The squared error (SE) is proper but not strictly proper; the text should avoid presenting SE and DS as equally principled as the strictly proper LS and CRPS rules.
  3. [Table 6] The reported LS differences between fit6b and fit5b are extremely small; add Monte Carlo standard errors or a formal comparison to support the claim that fit6b is clearly the best size model.
  4. [Section 2.2.3] The statement that aftershock PGA 'did not improve the results' is unsupported; please provide a summary of the comparison or a reference to an appendix containing the numbers.
  5. [Section 4.1.2 and Appendix D.2] The concavity sensitivity analysis is described only qualitatively; report a quantitative summary (for example, correlations between k_sn maps for different concavity values) to substantiate the claim that the results are unchanged.
  6. [Minor language issues] The text refers to 'Appendix 20' where 'Appendix D.2' is intended, and the reference to 'Gorhka' should read 'Gorkha'; please proofread the bibliography and cross-references.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central ksn–landslide association is estimated from a DEM-derived covariate rather than defined from the response, and model comparisons are checked by cross-validation.

full rationale

The paper's central claim—that elevated ksn is associated with landslide susceptibility but not magnitude—is not circular. ksn is computed from the Copernicus DEM via LSDTopoTools (Section 2.2.1), not from the landslide inventory, so the covariate is not defined in terms of the response. The susceptibility and size models are estimated from the observed centroid and log-area data, and the no-association-with-size conclusion is supported by cross-validated score comparisons of models with and without ksn (Tables 5-6), not by construction. The 'preliminary analyses' in Section 3.3 that guided transformations and removed ksn from the size models are in-sample model-selection steps, which could inflate apparent effects, but they do not reduce the claim to a definition; the grid and thinning CV provide an independent check. Self-citations to inlabru (Lindgren et al., 2024) and Suen et al. (2025) are software and methodological citations; the one load-bearing technical detail (mesh resolution based on Suen et al., 2025) is a numerical simulation result and not a self-referential uniqueness claim. The acknowledged limitation in Section 4.3.4 that omitted spatial random effects may allow spatially structured variability to be absorbed by covariates is a confounding/identifiability concern, not circularity. No specific equation or fitted parameter can be exhibited that makes a predicted quantity equal to its input by construction.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard geomorphic assumptions about ksn (stream power law, fixed concavity) and on statistical modeling assumptions (Poisson process, completeness of the inventory). No new physical entities are introduced. The concavity index and the manual ksn substitution are the main free choices that could influence the reported association.

free parameters (2)
  • Concavity index theta = 0.5
    Fixed value used in ksn computation; sensitivity to 0.4 and 0.6 was checked, but the chosen value is a modeling assumption, not fitted to landslide data.
  • ksn hanging valley substitution rule = not quantitative
    Manual replacement of ksn values in hanging valleys with nearby 'geomorphologically similar' values (Section 2.2.2, Fig. 15) is a subjective data modification that can affect the covariate.
assumptions (5)
  • domain assumption Stream power law and steady-state landscape assumption for ksn (Eq. 1)
    ksn is only meaningful if channel slope scales with drainage area via S = ksn A^{-theta}; the paper cites support but this is an assumption.
  • domain assumption Landslide centroids follow a Poisson point process with intensity lambda
    Used in Section 3.2 for the likelihood; ignores possible clustering or dependence beyond covariates.
  • domain assumption The inventory is spatially unbiased and complete enough for centroid analysis
    The paper acknowledges size censoring but still uses all centroids without correction.
  • domain assumption DEM topography is independent of the landslides (pre-event DEM)
    Copernicus DEM may contain post-earthquake topography; the paper does not address this.
  • domain assumption PGA from the mainshock is the relevant seismic trigger
    Aftershock PGA was tested and dropped; the inventory mixes events but lacks time stamps for individual landslides.

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Cite this review

Pith. "Pith review of Influence of river incision on landslides triggered in Nepal by the Gorkha earthquake: Results from a pixel-based susceptibility model using inlabru." pith.science (2026). https://pith.science/paper/HD5WB2WU

@misc{pith2026250708742,
  author       = {Pith},
  title        = {Pith review of: Influence of river incision on landslides triggered in Nepal by the Gorkha earthquake: Results from a pixel-based susceptibility model using inlabru},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HD5WB2WU}},
  note         = {Machine review of arXiv:2507.08742}
}
abstract

This study presents a comprehensive framework for modelling earthquake-induced landslides (EQILs) through a channel-based analysis of landslide centroid distributions. A key innovation is the incorporation of the normalised channel steepness index ($k_{sn}$) as a physically meaningful and novel covariate, inferring hillslope erosion and fluvial incision processes. Used within spatial point process models, $k_{sn}$ supports the generation of landslide susceptibility maps with quantified uncertainty. To address spatial data misalignment between covariates and landslide observations, we leverage the inlabru framework, which enables coherent integration through mesh-based disaggregation, thereby overcoming challenges associated with spatially misaligned data integration. Our modelling strategy explicitly prioritises prospective transferability to unseen geographical regions, provided that explanatory variable data are available. By modelling both landslide locations and sizes, we find that elevated $k_{sn}$ is strongly associated with increased landslide susceptibility but not with landslide magnitude. The best-fitting Bayesian model, validated through cross-validation, offers a scalable and interpretable solution for predicting earthquake-induced landslides in complex terrain.

Figures

Figures reproduced from arXiv: 2507.08742 by the authors.

Figure 1
Figure 1. Landslides (in red) induced by the 2015 Gorkha Earthquake ( [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Histogram of landslide centroid count against log(landslide area) in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Exploratory figures for basin 14982 showing channel steepness index ( [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figures from the paper (18 more)
Figure 4
Figure 4. Figure 4: Exploratory visualizations for basin 15329 showing channel steepness ( [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]
Figure 5
Figure 5. Figure 5: Example of populations of log ksn calculated for three different concavity values (m n) m/n = 0.4, 0.5, 0.6 from left to right as in basin 14982. in stable areas. In contrast, the CRPS, which is more robust to outliers, provides a broader measure of model accuracy. The…
Figure 6
Figure 6. Figure 6: Logarithmic Score (LS) differences for landslide centroid models across cross-validation settings, [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]
Figure 7
Figure 7. Figure 7: Continuous Ranked Probability Score (CRPS) differences for landslide centroid models across cross [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]
Figure 8
Figure 8. Figure 8: Empirical cumulative distribution function (ECDF) of Logarithmic Scores (LS) differences for [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]
Figure 9
Figure 9. Figure 9: Empirical cumulative distribution function (ECDF) of Continuous Ranked Probability Score [PITH_FULL_IMAGE:figures/full_fig_p022_9.png]
Figure 10
Figure 10. Figure 10: Empirical cumulative distribution function (ECDF) of Logarithmic Scores (LS) differences for [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]
Figure 11
Figure 11. Figure 11: Model fit6a for the full set of landslide centroid observations, based on 100 posterior samples. See [PITH_FULL_IMAGE:figures/full_fig_p027_11.png]
Figure 12
Figure 12. Figure 12: Model fit6b for the full set of landslide size observations, based on 100 posterior samples. See [PITH_FULL_IMAGE:figures/full_fig_p029_12.png]
Figure 13
Figure 13. Figure 13: Posterior estimates of the smoothed log ksn (left) and PGA (right) covariate effects using an RW2 prior, illustrating the non-linear relationships in fit6a using the full dataset. 4.3.5 Selected Basins Case Study It is important to note that the susceptibility map rep…
Figure 14
Figure 14. Figure 14: Zoomed-in posterior susceptibility mean fields from model [PITH_FULL_IMAGE:figures/full_fig_p032_14.png]
Figure 15
Figure 15. Figure 15: A: Landslide centroids falling into glacier landscapes for basin 2228 with basemap tile layer from ESRI World Imagery. B: ksn basin map with failure of algorithm due to glacier landscapes. C: ksn basin map after filling underperforming area with nearest neighbour valu…
Figure 16
Figure 16. Figure 16: Train Test Data Split for Cross Validation with grid size 3km [PITH_FULL_IMAGE:figures/full_fig_p037_16.png]
Figure 17
Figure 17. Figure 17: Scatter Plot of log landslide size against flow distance to channel (fd2ch) coloured by log [PITH_FULL_IMAGE:figures/full_fig_p038_17.png]
Figure 18
Figure 18. Figure 18: Scatter Plot of log landslide size against relief to channel (rf2ch) coloured by log [PITH_FULL_IMAGE:figures/full_fig_p039_18.png]
Figure 19
Figure 19. Figure 19: Channel characteristics and analysis for basin 22048. [PITH_FULL_IMAGE:figures/full_fig_p040_19.png]
Figure 20
Figure 20. Figure 20: Examples of log ksn distributions for selected basins under varying channel concavity values m/n (mn). 41 [PITH_FULL_IMAGE:figures/full_fig_p041_20.png]
Figure 21
Figure 21. Figure 21: Computation time for all models in all cross-validation (CV) settings [PITH_FULL_IMAGE:figures/full_fig_p042_21.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.