E3S Web of Conferences 415, 07009 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341507009

Debris Flow Hazard Mapping Along Linear Infrastructure: AnAgent Based Model and GIS Approach
Graham Knibbs1*, Richard Guthrie2 , and Thad Wasklewicz3
1Stantec Consulting Ltd., Geohazards and Geomorphology, Burnaby, British Columbia, Canada
2Stantec Consulting Ltd., Geohazards and Geomorphology, Calgary, Alberta, Canada

3Stantec Consulting Ltd., Geohazards and Geomorphology, Fort Collins, Colorado, United States of America

Abstract. Often linear infrastructure, including rail, highways, and pipelines, span large geographic areas
intersecting a variety of terrain, predisposing infrastructure to a higher likelihood of geohazard interaction.
Debris flow models can be particularly advantageous in remote hazard and risk mapping along linear
infrastructure as runout from susceptible slopes may extend considerable distance downslope to a receptor.
In this sentiment, a method is developed using an agent-based model, DebrisFlow Predictor, in combination
with geographic information software (GIS), to produce regional debris flow hazard and risk profiles alongwidespread corridors. Thousands of debris flows upslope of a receptor(s) are simulated in the model
environment (i.e., model scenarios). Outputs of the modelled scenarios provide probabilistic spatial
attributes of debris flow runout and depth across a digital elevation model at a 5m resolution. The outputsof multiple scenarios are mosaiced and corrected to in-situ temporal and spatial debris flow initiation
conditions in GIS. The corrected scenario outputs provide a comprehensive hazard profile along theinfrastructure alignment, that in turn can facilitate quantified vulnerability and risk calculations. Thousandsof modelled debris flows throughout several physiographic regions of Canada and the United States ofAmerica, calibrated to local conditions, provide substantive support for a novel methodology to identify key
hazard and risk locations to major linear infrastructure.

1 Introduction
The novel methodology outline by this paper wasdeveloped using a specific agent-based model,
DebrisFlow Predictor; however, it should be clarified
the method is model agnostic, so long as the model has
the functionality to provide probabilistic spatial outputsof runout occurrence and depth.
1.1 DebrisFlow Predictor Primer
Often linear infrastructure, including rail, highways, andpipelines, span large geographic areas intersecting avariety of terrain, predisposing infrastructure to a higher
likelihood of geohazard interaction. Debris flow models
can be particularly advantageous in remote hazard andrisk mapping along linear infrastructure [1-3].
DebrisFlow Predictor (DFP) is a shallow landslide
runout software that provides probabilistic spatial
outputs of deposition and scour along a simulated
landslide path. The path, or rather simulated runout, isproduced by agents interacting with the topographic
conditions of a 5-metre digital elevation model (DEM),
and other surrounding agents in the model environment.
These interactions are defined by a set of empiricallyderived distribution curves [4]. As an agent moves
downslope through a series of time-steps, it makes
decisions to entrain or deposit sediment along its route.

Running the simulation from static initiation locations
results in probabilistic runout paths, that can be exportedout of the model environment to GIS for furtheranalysis.
1.2 Hazard Primer
The definition of hazard varies throughout disciplines,
making it a necessity to define the term in the context ofits use [3]. The definition formally adopted by the UN
Office of Disaster Risk Reduction (UNDRR), ‘a
process, phenomenon or human activity that may cause
loss of life, injury or other health impacts, property
damage, social and economic disruption orenvironmental degradation’ [5]. In this context and forthe purposes of defining hazard (HT,S,R) in this paper as
it relates to debris flows, the term can be considered asa three-part function, whereby:
HT,S,R = HT × HS × HR

(1)

HT is the probability of landslide initiation per unitof time, HS is the spatial probability of landslide
initiation per unit area and HR is the likelihood that thehazard will reach a portion of the landscape; HR is
further defined by a function of two factors, that areprovided later.

* Corresponding author: graham.knibbs@stantec.com© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 07009 (2023)
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https://doi.org/10.1051/e3sconf/202341507009

2 Method and Discussion

situ landslide density and event interaction in eachindividual scenario).
Once the scenarios are developed in GIS, they areimported into the model environment and run amultitude of times (also referred to as looping). The
number of loops completed for each scenario is reliant
on assessor’s judgement to balance the processing
expense of the model and assessment goals. Aggregatedoutputs from each looped scenario, that include thespatial occurrence and depth information, are thenexported from the model environment and imported toGIS for further analysis.
Within GIS, modelled debris flow depth results areconverted to raster format and averaged using common
overlay analysis methods. Average depths can then belater used to facilitate vulnerability, or rather
consequence and ultimately risk, calculations along thereceptor [9,10].
Determining the average runout, or HR, requires
additional processing steps and is somewhat more
abstract. Because multiple scenarios were run fromvarying initiation points across the region, and in someinstances not all scenarios interact at the same location,
the probability of the runout occurrence within eachdiscrete scenario and the probability of runout
occurrence within the overall modelled scenario spacemust be reconciled. This can be referred to as the interscenario probability (PRun) and the intra-scenario
probability (PScenario), respectively, whereby the functionof these two probabilities results in the overall runout
probability (HR) of the modelled conditions. This can be
expressed as the following:

2.1 Determining Runout Hazard (HR)In consideration of equation (1), modelled outputs areused in combination with GIS to determine HR. The firststep in the process is to define initiation locations for thelandslide simulations; in this instance, a grouping ofinitiation locations run under a similar set of calibration
parameters in the model is referred to as a scenario.
To create scenarios, GIS is used to identify
susceptible ground and define debris flow initiation
locations; whereby susceptible ground is terrain wheredebris flows may occur. While there are many methodsof delineating susceptible ground and probable debris
flow initiation locations [6-8], the overall intent of thisselection exercise is to provide an adequate spatial
density of landslide initiation points upslope of thereceptor. The density of initiation locations must be suchthat the intersecting runout at the receptor can beconsidered irrespective of the initiation location – thisconcept is later discussed. To propagate initiation
locations for scenarios, a fishnet grid of points is draped
across the region, at a defined interval spacing. Thosepoints within the grid that intersect defined susceptible
ground are then extracted as initiation locations and used
to develop scenarios (Fig.1). In most instances, a 150metre spacing is a good starting point at a regionallandscape scale to balance the spatial density andprocessing expense of the model; however, it is notuncommon to adjust this spacing based on the regional
conditions and model capacity.

HR = PRun × PScenario(2)

Whereby at any given pixel location in the model:

And,PRun = (∑𝐸𝐸𝐸𝐸)/((∑𝑆𝑆𝑆𝑆) × 𝑅𝑅𝑅𝑅)
PScenario = (∑𝑆𝑆𝑆𝑆)/𝑆𝑆(3)(4)

Whereby,Ec = Number of times that a pixel location wasintersected by an agent in all model scenarios (e.g., Outof four scenarios run 100 times each, a pixel wasintersected fifty times in the first scenario, one-hundred
times in the second, three times in the third and no times
in fourth. Ec in this example is 153).

Fig. 1. Example of selected initiation locations (red points)
for model scenarios relative to susceptible ground (green).

The selected initiation points are then grouped into
scenarios by assigning a random number between a user
defined ranged. The range of scenarios shouldadequately divide the initiation locations into groups
that account for the complexity of terrain and landslide
processes in the region, with the overall intent of
reducing landslide interaction in each individual
scenario simulation. This step is often reliant on assessor
judgement of in-situ or remote imagery observations oflandslide density in individual catchments (i.e., theassessor must increase or decrease the range of possible
scenario groupings to better replicate the observed in-

Sc = Number of scenarios that intersected the rasterpixel, or ‘scenario count’. SC is three using the example
above.
Rc = Total number of runs completed for one scenario.
Referring to the example, each scenario was run 100times, so Rc is 100.
S = Total number of scenarios completed. Continuingwith the example, S is equal to four.

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By these means, HR at any discrete location isindependent of the debris flow initiation location to adegree of uncertainty, that include the model andassessment limitations. Rather, if the assessor wassuccessful in scenario development, a sufficient densityof landslides should be simulated upslope of the receptor
throughout the course of all scenarios, such that theconvergent and divergent topography encountered by
the landslide agents as they travel downslope in themodel environment, concentrate the variability ofrunout, and ultimately accommodate for other possible
initiation locations within that catchment that were notsimulated [11]. This assertion is further bolstered by aMonte-Carlo analysis of runout in the model space, andthe necessity for the assessor to balance the number ofmodelled runs and initiation density of the scenarios tosatisfy the accuracy goals of the assessment. Simply, thedenser landslide initiation grouping is in each scenario,
and the more travel time each agent has in the model,
the more reliant HR results will become.

To accomplish this, the assessor must establish thein-situ HT,S of the study area. This can be completed
through many different methods, which are not the topicof this paper, but generally can be facilitated with alandslide inventory or field assessment [12,13]. It
should be apparent that HT,S, or recurrence interval,requires
timeandareaunits(e.g.,landslides/hectare/year).
Once HT,S is determined, the assessor can utilize thebinomial probability formula (eq. 5) to determine theprobability of a discrete landslide initiation scenario. For
example, in most assessments it may be important for
the assessor to understand the probability of ‘at least one
landslide’ occurring; however, varying assessment
goals may constitute determining other landslide
initiation probabilities. Foregoing hypotheticals, theassessor can simply adjust the binomial probability
equation as needed for a varying amount of landslide
initiations to suit the assessment goals. In an instance
where HT,S probability nears or exceeds one, anexceedance probability should be utilized in lieu of thebinomial probability formula; however it is rarely thecase to have such a high HT,S probability in a widespread regional assessment. For the purposes ofdiscussion, the binomial probability formula below isdefined for at least one successful event, or rather,landslide initiation within a region.
P(x≥1) = P(x=1) + P(x=2) +P (x=3)…+P(x=n) (5)P(x) = nCxpx(1-p)n-x(6)Whereby,n = Number of trials, or rather study area size, for which
a successful event may occur (e.g., if a study area is 10
km2, n = 10)
x = The interested number of successful trials, orlandslide initiations (e.g., 0, 1, 2, 3, 4…)
p = Probability of success in a single trial, or rather thein-situ HT,S probability determined by the assessor.
Once the binomial probability is established for agiven number of landslide occurrences, that represents
the in-situ HT,S condition, the probability must becorrected to reconcile the modelled scenario conditions
before multiplying it by HR. Rather, it is likely that amagnitude, or more, of landslides were initiated in eachscenario in the modelled environment relative to the insitu conditions, and thus, a correction factor must beapplied to the binomial probability to ensure the factorsof hazard (eq.1) are equivalent. This is simply
accomplished by dividing ‘x’, from equation 5 above, by
the average number of agents in all scenarios andmultiplying that value by the discrete probability
determined for the corresponding ‘x’ trials. The
corrected probability, now representing the HT,S
probability of the modelled conditions, can bemultiplied by HR to determine the comprehensive hazard
profile, or HT,S,R (Fig.3).

Fig. 2. Example of HR probability as determined fromscenario locations depicted in Figure 1.

2.2 Combining Runout Hazard (HR) with Hazard
in Time and Space (HT,S) to Determine
Comprehensive Hazard (HT,S,R)
The means of calculating HR result in a unitless
probability that is ultimately independent of the upslope
initiation location. In this respect, HR determined for themodel space, must be corrected to accommodate for thein-situ hazard in time and space, or HT,S,, if theassessment goal is to provide comprehensive hazard(i.e., HT,S,R).

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6.

Gov. of B.C. Resources Inventory Committee, inGuidelines and standards for terrain mapping in
British Columbia, Victoria (1996)
7. T.P. Rollerson, T. Millard, and B. Thomson, in
Using terrain attributes to predict post-logging
landslide likelihood on southwestern Vancouver
Island, B.C. Ministry of Forest Research Section,
Nanaimo (2001)
8. X. Chen, H. Chen, Y. You, et al. Environ. Earth
Sci., 75, 70 (2016)
9. R.L. Ciurean, H. Hussin, C.J. van Westin, M.
Jaboyedoff, P. Nicolet, L. Chen, S. Frigerio, T.
Glade, Nat. Haz., 85, 929-957 (2017)
10. M. Kim, J.H. Kwak, Water, 12, 7 (2020)
11. R.H. Guthrie, A. Hockin, L. Colquhoun, T. Nagy,
S.G. Evans, C. Ayles, Geomorph., 114, 601-613(2010)
12. M. Jakob, S. Bale, S. McDougall, P. Friele.
Regional frequency– magnitude curves for debris
flows and debris flood, in GeoVancouver (2016):
69th Canadian Geotech. Con., Vancouver (2016)
13. O. Hungr, S. McDougall, M. Wise, M. Cullen,Geomorph., 96, 355-365 (2008)
14. S. McDougall, Canadian Geotech. Jour., 54, 605620 (2016)

Fig. 3. Example of HT,S,R probabilities following correction toHR shown in Figure 2. Note, the inverse of the probabilities
shown would represent the recurrence interval of hazard.

3 Conclusion
New methods for remotely assessing hazard are
becoming available as processing capacity and higher
resolution data become readily accessible [14]. The
approach of utilizing a novel agent-based model, such as
DebrisFlow Predictor, in such a manner has enabled thequantification of probabilistic hazard results acrosswidespread regions with modest limitations andarguably astounding visual aids in support ofcommunicating results. Quantified spatial hazard
information also translates to a means for qualified
professionals to quantify risk, in most facets, providing
communities, government agencies, and industry withquantitative data to make informed decisions onmitigation.
The authors of this paper would like to acknowledge ongoingproject funding and collaboration with Trans Mountain
Pipeline L.P. and Innovation Solutions Canada during thedevelopment and refinement of these methods.

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