E3S Web of Conferences 415, 05026 (2023)
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https://doi.org/10.1051/e3sconf/202341505026

Quantifying debris-flow hazard and risk based on fan sector
Alex Strouth1,2*, Sophia Zubrycky2,3, and Scott McDougall2
1BGC Engineering Inc., Golden, Colorado, USA

2The University of British Columbia, Vancouver, British Columbia, Canada
3BGC Engineering Inc., Vancouver, British Columbia, Canada

Abstract. We show how a quantitative estimate of debris-flow hazard and risk can be derived simply fromthe position of infrastructure on the fan relative to the fan apex and the most likely flow path (e.g., activechannel). Fan sectors and the spatial probability of impact in each sector are based on a fan-normalized heatmap of debris-flow impacts derived from 146 mapped impact areas across 30 fans in southwestern British
Columbia, Canada. As a proof-of-concept, we provide an example for annual life loss risk to an individual
who occupies a home in various sectors of a debris-flow fan. The results are comparable to broad findings
from quantitative risk assessments completed at 10 fans in British Columbia and Alberta, Canada withsimilar characteristics. The method presented here is a way to obtain a high-level quantitative risk estimate
prior to a detailed site-specific assessment.

1 Introduction

2.

Much of the information needed to characterize debrisflow hazard is recorded within, or can be derived from,the debris-flow fan. For example: frequency-magnituderelationships are recorded in fan stratigraphy andvegetation and can be estimated from the fan volume orarea [1]; flow depths can be derived from fanstratigraphy; maximum travel distance is recorded by
the fan boundary; and flow path and potential avulsion
locations are controlled by the fan topography andchannel position. We hypothesize that quantitative
estimates of debris-flow hazard and risk, such as impact
probability, impact intensity, vulnerability, and life loss
probability, can be derived simply from the position of
infrastructure on the fan relative to the fan apex and themost likely flow path (e.g., active channel).
Although debris-flow hazard and risk assessments
are revolving more and more around numerical models(at least in our region of North America), empirical
datasets that characterize debris-flow fans will always
be needed to inform selection of input parameters and tovalidate model results. In fact, for many risk
management situations, empirical-statistical analysis of
the fan landform is a sufficient and efficient method forreaching a well-informed decision. Therefore, we areresearching how to use simple characteristics of a fan todirectly inform estimates of debris-flow hazard and risk.
In this paper, we will:
1. Introduce the concept of “fan-normalizedspace” and demonstrate how it can be used tocompare spatial hazard and risk trends across
fans.

3.

Introduce a method to quantify life-loss risk tohouses based on their relative location on a fan.
Compare the results to quantitative risk
assessments completed in British Columbia andAlberta, Canada.

2 Fan-Normalized Space
Zubrycky et al. [2] present a method to extract andvisualize spatial impacts of debris flows on fans using a“fan-normalized space”. The method uses a circularmeasurement grid centred on the fan apex andnormalized by the maximum down-fan length andmaximum cross-fan arc length (Fig. 1). The fannormalized space normalizes a location on the fansurface based on its position down-fan and cross-fan.
The maximum fan dimensions are interpreted to be
the statistical upper bound of runout from the fan’s
formative debris flows. Zones of increasing radii
represent mobility down-fan. Arc length offsets
represent lateral shifts across the fan relative to theprevious debris-flow path. Previous debris-flow paths
are often, but not always, represented by the current
channel position.
Impact areas plotted in fan-normalized spacehighlight the typical runout distance and location andextent of avulsion impacts relative to the fan boundary.
Multiple impact area plots can be combined for a fan ora group of fans to create a composite spatial impact heatmap. Zubrycky et al. [2] created a composite spatial
impact heat map for 146 impact areas across 30 debrisflow fans in southwest British Columbia, Canada (Fig.
2). The heat maps capture regional frequency–* Corresponding author: astrouth@bgcengineering.ca© 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, 05026 (2023)
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https://doi.org/10.1051/e3sconf/202341505026

magnitude distributions, mobility behaviours, andavulsion behaviours specific to fans in the study area.
These heat maps highlight areas on the fan that are mostsusceptible
todebris-flow
impact,without
differentiation between debris-flow magnitude, flow
thickness, composition, or speed.
Although we have not done so yet, otherobservations and estimates could also be plotted in fannormalized space, such as deposit thickness, flow
velocity, and vulnerability of buildings, infrastructure,and people. Trends in these data could be used to inform
assessments of debris-flow hazard and risk toinfrastructure and people, based on the relative locationof these elements to the fan boundaries and previous
debris-flow path.
For fans in a similar environment, and when pairedwith geomorphic interpretation and judgement, theseobservations can support quantitative estimates ofdebris-flow hazard in several ways. The heat map (Fig.
2) provides an estimate of susceptibility to debris flow
impact for various fan sectors. This information
supports qualitative and quantitative hazard assessments
and debris-flow hazard mapping. With one additional
step, a quantitative estimate of spatial impact probability
can be derived by multiplying the susceptibility value by
the average annual probability of a debris flow reaching
the fan apex. Although the fan boundary is an imperfectnormalizer (e.g., in the case of truncated fans), the fan
landform and main channel can be identified reasonably
consistently for the purpose of forecasting.

Fig. 2. Spatial impact heat map at 30 debris-flow fans in
British Columbia, Canada [2]. Dashed lines are interpreted
isolines of spatial impact frequency.

3 Estimated Risk by Fan Sector
We hypothesize that life-loss and direct damage risk
related to debris flows could be estimated quantitatively
based on the location of elements at risk in fannormalized space. As a proof-of-concept, we provide an
example for annual life loss risk (R) to an individual
who occupies a home on a debris-flow fan, which is theproduct of [3]:- H: Annual probability of a debris flow reaching thefan.
- S: Conditional probability that the home is reachedby the debris flow.
- T: Conditional probability that the person is homewhen the debris flow occurs.
- V: Conditional probability that the person is killed
if they are impacted by the debris flow (i.e.,vulnerability).
H and T are independent of the home’s location on
the fan. H can be approximated based on the historicaland vegetation record. In southwest British Columbia,
many fans the authors have studied experience debris
flows at a frequency in the range of 10 to 100 years. T
can be approximated by the amount of time that theperson most at risk spends at home. In the absence ofother information, we assumed this value to be 70% to80%.
S is a function of the home’s location on the fan. We
partitioned the fan into sectors to simplify selection ofan S value (Fig. 3) and estimated ranges of S directlyfrom the spatial impact heat map (Table 1).
We hypothesize that V could also be approximatedbased on fan sector because debris flows decelerate froma peak velocity near the fan apex to a stop before thedistal fan margin. Therefore, it follows that impact

Fig. 1. Fan-normalized space for one impact area relative tothe previous flow path.

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E3S Web of Conferences 415, 05026 (2023)
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Table 2. Assumed range of flow parameters to inform
selection of V based on debris flow intensity and damage
class [4]. Depth [m], Velocity [ms-1], Intensity [m3s-2].

intensity, building damage state, and probability ofdeath are at a maximum near the fan apex and at aminimum in fan sectors that are on the distal fan, farfrom the channel. Since a similar heat map to Fig. 2 for
V is not available, we estimated ranges of debris flow
depths and velocities for the fan sectors typical of
granular debris flows we have studied in southwest
British Columbia. We then related the intensity (in termsof depth x velocity2) to building damage class using
methods from Jakob et al. [4] and estimated ranges of Vfor each building damage class (Table 2).
Using average values for S, T, and V, we calculate
R to an individual who occupies a home on a fan withan average debris-flow frequency of 100 years (Table3). In this region of Canada, individual life loss risks thatare greater than 100 micromorts per year (i.e., 1 in10,000 per year) are often considered to be intolerable
for existing developments [3]. Therefore, Table 3
suggests, as a rule of thumb, that in the absence ofmitigation, houses near the fan apex and near thechannel will generally have intolerable life loss risk.
Houses on the distal and mid fan far from the channel
will generally have tolerable life loss risk.

Near main channel
UpperFan

Depth: 3-5
Velocity: 7-10
Intensity: 150-500
Damage class:Complete destruction
V: 0.9Mid
Fan

Depth: 1-3
Velocity: 5-7
Intensity: 25-150
Damage class: Major
structural damage tocomplete destruction
V: 0.5-0.9
Depth: 0.5-2
Velocity: 2-5
Intensity: 2-50
Damage class: Someto major structural
damageV: 0.1-0.5

DistalFan

On fan, outside ofmain channel area
Depth: 1-3
Velocity: 5-7
Intensity: 25-150
Damage class: Major
structural damage tocomplete destruction
V: 0.5-0.9
Depth: 0.5-2
Velocity: 2-5
Intensity: 2-50
Damage class: Some tomajor structural
damageV: 0.1-0.5
Depth: 0.1-1
Velocity: 1-3
Intensity: 0.1-10
Damage class: Somesedimentation to somestructural damage
V: 0.01-0.1

Table 3. Estimated annual life loss risk (R) in micromorts
based on fan sector to an individual who occupies a home on
a debris-flow fan with an average debris-flow frequency of
100 years. 1 micromort = odds of 1 in 1,000,000 per year [3].
Risk (R)(micromorts)
Main channel
Within 10% of
the fan angle
from the mainchannel
Within 10% to25% of the fanangle from theactive channel
Beyond 25% of
the fan angle
from the activechannel

Fig. 3. Fan sectors used in the risk calculation.
Table 1. Estimated range of S for fan sectors based on datafrom 30 fans in southwestern British Columbia, Canada [2].

Main channel
Within 10% of thefan angle from themain channel
Within 10% to 25%of the fan angle fromthe active channel
Beyond 25% of thefan angle from theactive channelUpper
FanMidFanDistalFan

0.8-1

0.5-0.8

0.05-0.5

0.5-0.8

0.2-0.5

0.05-0.3

0.1-0.5

0.1-0.2

0.01-0.1

0-0.1

0-0.050-0.01Upper
FanMid FanDistal Fan

6,100

3,400

600

3,400

800

70

1,600

300

20300

60

2

Quantitative risk assessments (QRAs) carried out by
BGC Engineering Inc. (BGC) during the last decadealso suggest there is a relationship between the fansector and quantitative risk value. From a review ofQRAs completed at 10 fans located in British Columbia
and Alberta, Canada (characteristics summarized inTable 4), we found R tends to be:- >1,000 micromorts (i.e., >1 in 1,000) per year near
the fan apex and mid-fan near the channel.
- 100 to 1,000 micromorts (i.e., 1 in 10,000 to 1 in1,000) per year in the distal fan near the channel.
- < 100 micromorts (i.e., <1 in 10,000) per year in themid and distal fan far from the channel.
These risk values from the QRAs accord with theestimated risk by fan sector values presented in Table 3.

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Table 4. Typical characteristics of debris-flow fans where
life loss risk was quantified by BGC.
Item
Return period of debris
flows large enough to cause
life loss
Return period of largest
debris flow considered in
the risk estimate-Estimating total debris-flow risk across a large
region, for example, to compare with historical
records and to allow calibration of site-specificestimates.
- First order inferences at specific sites to guidepreliminary decisions and for scoping more detailed
assessments.
Although the estimates are highly approximate, they
provide quantitative values that can be used to compare
debris-flow risks to other hazards and to estimate thejustifiable cost of risk reduction measures [6].
More research is needed to fully develop these tools,
and we encourage others to collect and publish data fromother world regions. Research needs include:- Collecting flow intensity, vulnerability, andquantitative individual risk estimates from a variety
of settings and plotting them in fan-normalized
space.
- Identifying spatial patterns and relationships
between fan and infrastructure characteristics andhazard and risk values.
- Developing heat maps in fan-normalized space, likeFig. 2, to illustrate the spatial patterns.

Description
10 to 100 years
1,000 to 3,000 years

Volume of debris flows
considered

1,000 to 5,000,000 m3

Building type

Wood frame, single family
homes, without local
debris flow impact
protection

Fig. 4 is an example map of life loss risk that was
created for one of these projects. It has several
characteristics that are common to all the QRAs in thatrisk values are greatest near the fan apex and near themost likely flow path, and smallest on the distal fan far
from the most likely flow path. In this case, the mostlikely flow path identified through numerical modellingis not the current stream channel. Engineering
judgement is required when using the fan sector
approach for risk estimation, such as selecting the mostlikely flow path (which may not be the main channel)
and adjusting spatial probabilities (Table 1) based on
topography.

References
1.
2.
3.
4.
5.

6.

Fig. 4. Example life loss risk estimate map for individuals
within homes at Cold Spring Creek, British Columbia [5].

4 Discussion
The heat map of spatial impact and estimated life loss
risk by fan sector are specific to the region in which they
were developed. Even within that region, they do not
replace a detailed, site-specific risk assessment.
Nevertheless, approximate estimates like these could
have many uses, including for:- Regional prioritization studies that attempt toidentify the highest risk fans and quantify risk
levels.
- Regional planning studies that attempt to identify
the number of individuals at certain risk levels.

4

M. Jakob, E. Mark, S. McDougall, P. Friele, C.-A.
Lau, & S. Bale. Earth Surf. Process. Landf. 45, 12,2954–2964 (2020)
S. Zubrycky, A. Mitchell, S. McDougall, A.
Strouth, J.J. Clague, B. Menounos. Earth Surf.
Process. Landf. 46, 12, 2395-2413 (2022)
A. Strouth, S. McDougall. Landslides 19, 4, 977991 (2022)
M. Jakob, D. Stein, M. Ulmi. Natural Hazards, 60,2, 241-261 (2011)
BGC Engineering Inc., Cold Spring Creek Fan
Debris Flow, Quantitative Risk Assessment. Finalreport for Regional District of East Kootenay,Canada, (2021)
A. Strouth, S. McDougall. Landslides 18, 3, 10711085 (2021)