Modelling the control of groundwater on landslides triggering: the respective role of atmosphere and rainfall during typhoons

. Landslides are often triggered by catastrophic events, among which earthquakes and rainfall are the most depicted. However, very few studies have focused on the effect of atmospheric pressure on slope stability, even though weather events such as typhoons are associated with significant atmospheric pressure changes. Indeed, both atmospheric pressure changes and rainfall- 10 induced groundwater level change can generate pore pressure changes with similar amplitude. In this paper, we assess the respective impacts of atmospheric effects and rainfall over the stability of a hillslope. An analytical model of transient groundwater dynamics is developed to compute slope stability for finite hillslopes. Slope stability is evaluated through a safety factor based on the Mohr-Coulomb failure criterion. Both rainfall infiltration and atmospheric pressure variations, which impact slope stability by modifying the pore pressure of the media, are described by diffusion equations. The models have then 15 been forced by weather data from different typhoons that were recorded over Taiwan. While rainfall infiltration can induce pore pressure change up to hundred kPa, its effects is delayed in time due to diffusion. To the contrary, atmospheric pressure change induces pore pressure changes not exceeding a few kPa, but its effect is instantaneous. Moreover, the effect of rainfall infiltration on slope stability decreases towards the toe of the hillslope and is cancelled where the water table reaches the surface, leaving atmospheric pressure change as the main driver of slope instability. This study allows for a better insight of 20 slope stability through pore pressure analysis, and shows that atmospheric effects shouldn’t always be neglected. evenly distributed along hillslopes (Meunier et al., 2008), this work presents a 2D analytical model based on a hydrological model applied to a hillslope 50 and a mechanistic safety factor to evaluate atmospheric and rainfall effects on slope stability. We use this model in this paper to investigate the role of pore pressure changes induced by rainfall and atmospheric pressure changes during major storms on slope stability, while accounting for groundwater level, pre-conditioned by seasonal rainfall and compare it to the rainfall forcing. First, we define a slope stability model based on a classical Mohr-Coulomb criterion. As both rainfall and atmospheric effects 55 implies pore pressure diffusion in groundwater, the link to slope stability requires a specific model. We therefore define an analytical solution for groundwater flow in a finite hillslope, and accordingly apply infiltration and atmospheric induced pore pressures to compute slope stability changes. Second, we consider simple synthetic scenarios of pressure and rainfall changes to model their distinct contributions to slope stability. This allows to define spatial domains along the hillslope where the instability is predominantly driven by either rainfall or atmospheric pressure changes. Third, we apply this model to observed 60 meteorological data from Taiwan to compute the respective impact of different typhoons, through rainfall or atmospheric pressure change, on slope stability. Last, we discuss about the results and the relevance of the model. The event corresponds to a rainfall of 86.4 mm, during which the atmospheric pressure drops of 1 kPa.

My experience makes me most suited to comment on the groundwater hydrology aspects of this paper, rather than the landslide hazard component. In this respect I have a few concerns.
1. The hydrological model used in this paper is a combination of a Dupuit-Forchheimer (D-F) aquifer model and a one-dimensional infiltration model based on the Richards equation. After reading the paper I was left unclear on how exactly these two models interact, and what effects the transient component of the water table response has on their results. 2. There needs to be more careful attention paid to the relationship between this hydrological model and the expected groundwater dynamics of the landscapes the model intends to capture. (Steep landscape hillslope hydrology see e.g. Montgomery et al. (1997)). The linearized, horizontal-based form of the D-F model may be appropriate in low relief settings or for deep aquifers that respond slowly to recharge, but the landscapes considered here are steep, and recharge here is assumed to infiltrate instantaneously to the water table. 3. The two hydrological models operating together contain potentially contradictory information on the pore water pressure below the water table.
While I recognize that issues 2 and 3 are acknowledged in Discussion section 5.1, it seems that most of the paper does not meaningfully engage with these limitations. If the authors retain the current hydrological model, rationale and limitations of the model need to be more clearly stated up front in the introduction and methods sections. While I cannot comment on the novelty of the landslide hazards component of this paper, I was left with the impression that there is merit to exploring the processes they consider here, though I think the hydrological basis of this work could use more thought. I've added more details in the line-by-line notes below.

Line by line:
Title: Title feels a little unspecific -what about the atmosphere, and what about groundwater? Could I suggest something along the lines of: "Finite-hillslope analysis of landslides triggered by excess pore water pressure: the roles of atmospheric pressure and rainfall infiltration during typhoons"

Abstract:
Two things in the abstract seem contradictory to me. Please reconcile or clarify the following: Lines 10-11 you state that "atmospheric pressure changes and rainfall induced groundwater level change can generate pore pressure changes with similar amplitude," but then in line 17-18, you say they differ by perhaps several orders of magnitude. Lines 14-15 you state that "rainfall infiltration and atmospheric pressure variations" are described by diffusion equations, but then in line 18 you say the effects of atmospheric pressure are instantaneous. This may be a matter of the phrasing, but it is confusing.

Introduction:
Line 31: "cumulated rainfall" -> "groundwater recharge" Line 38: "Little attention has been by received by this potential slope destabilisation factor" -> "This slope destabilisation factor has received little attention." Line 40: "…modifying slope stability." Citation? Line 55-56: "As both rainfall and atmospheric effects implies pore pressure diffusion in groundwater, the link to slope stability requires a specific model." This sentence seems vague to me. Line 59: "allows us to define" Line 62: remove "about"

Methods:
Line 65: Not sure what "homogenous half space" means and it is not mentioned anywhere else in the text. Line 90: "Under rainfall constrain" ? Line 101: "hydrogeological model" usually refers to a model of the characteristics of an aquifer -it's permeability, porosity, stratigraphy and composition (e.g., Condon et al. 2021 5.1). Maybe hydrological model would be better? Line 101: I would use "slope" or "topographic slope" over "dip," because dip has a different geologic meaning. Line 104: Interesting, I have not seen this called the diffusivity equation before. Looking around online, it seems this term is more commonly applied in the petroleum industry to other fluids? In hydrology I see this called the Boussinesq equation (e.g. Troch 2013, paragraph 9, Boussinesq equation for horizontal aquifers) or simply the Dupuit-Forchheimer equation. Line 110: "storage" -> "storage coefficient" Line 112: "in term of" -> "in terms of" Line 119, 130: "in function of" -> "as a function of"  Iverson (2000) there are extensive assumptions and conditions required to reduce the Richards equation to this particular 1D diffusion form. These need to be identified and discussed. Line 138: "characterise" -> "characterised" Line 139: "model considered a 2D mode" Model? Consider rephrasing to avoid repetition. Line 141: "one-dimension" -> "one-dimensional" Lines 148-149: Could you more clearly state the boundary conditions to arrive at this solution? The constant loading gives the surface boundary condition, what is the condition at depth? Seems like this solution is not accounting for the water table depth? Line 152: tc = z2/D should this be \hat{D}? Line 154: "convoluted" -> "convolved" Line 167: Again more clearly state lower boundary condition. Line 168: change citation type to "Carslaw and Jaeger (1959)" Semantically, it also seems to me less that tc is underestimated, and more that it may not be the right quantity for comparison with the timescale estimated. Line 200: "slop" -> "slope" Line 214: Still unclear exactly how the water table rise during event is incorporated into your model.

Results -Application:
Line 247: "east of Taiwan" -> "eastern Taiwan" or "the east of Taiwan" Line 251: "inferior to" -> less than Line 255: "contrasted" -> contrasting Line 257: remove "has" Line 278: you say "amount of rainfall" which to me implies rainfall depths, but rates are given. I would make these agree. Line 290: "caps off" colloquial language, consider replacing Line 296: "in function of the event" what does this mean? Figure 6: The use of black and blue together in plots b-i is difficult to read. I would choose a better color contrast.

Discussion:
Line 314: "models limitations" -> "model limitations" Line 315: "considered in this study consider" rephrase Line 355: "has been" -> was Line 365: Worth mentioning in this section that the diffusivity in the 1D model is Iverson (2000)'s maximum hydraulic diffusivity, derived for conditions near saturation. Line 385: Can you provide some more physical insight here on why diffusivity affects these in opposite ways? Line 392: When considering only these two effects. Do you think atmospheric pressure effects could be more important than other mechanisms going on when hillslopes fully saturate, like seepage? (Found this, line 455-456) Lines 399: When you say that the response of psi_air is instantaneous, I think that then the pore pressure response to a gate function should just look like the gate function. But it seems like what you're implying is that there is no delay in the beginning of the response, even though there still is a decay of the response in time? Lines 406-408: How does this finding compare with literature? Do we see landslides occurring in these locations? Line 431: "dominants" -> dominant Line 443, 449: "repartition" Partitioning? Check word choice. Line 450: "typhon induced" -> "typhoon-induced" Line 478: weeks or months after the rain event -has this been observed? I think a reference would strengthen this argument. Line 489: "amount of cumulated rainfall" -> "depth of rainfall" or "accumulation of rainfall" Line 495: large variations in pore water pressure?