E3S Web of Conferences 415, 03009 (2023)
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https://doi.org/10.1051/e3sconf/202341503009

What does landslide triggering rainfall mean?
Richard Guthrie1*, Thad Wasklewicz2, Graham Knibbs3, Eric Hertzman3, Sanaz Imen4, David Bigelow5
1

Stantec Consulting, Geohazards and Geomorphology, Calgary, Canada
Stantec Consulting, Geohazards and Geomorphology, Fort Collins, US
3
Stantec Consulting, Geohazards and Geomorphology, Burnaby, Canada
4
Stantec Consulting, Innovation, Washington, US5
Jupiter Intelligence, California, US2

Abstract. Landslide-triggering rainfall thresholds are often subject to both false negatives (landslides where none areexpected) and false positives (no landslides despite thresholds being exceeded). Debris flows and shallow landslides
impact communities and infrastructures worldwide. Refinement of the relation between rainfall intensity and landslide
occurrence would help remove the imprecise nature of this tool moving forward. Continuous 6-hour gridded
precipitation data from over a five-year interval 900 km2, combined with a complete, time-constrained, landslide database over the same period, are used to derive relations for the probability of shallow landslides with rainfall intensity
measured over 6-hour, 12-hour, or 24-hour durations. Previously published and widely used thresholds are quantified interms of landslide probability per unit area and demonstrate, for different sized study areas, the likelihood that at least
one landslide will be initiated at different intensities and durations. Probabilistic distribution of landslides for a given
study area and rainfall intensity can be easily derived using the binomial method from these relations.

1 Introduction
Rainfall and shallow landslides relationships have beenstudied for the past 40+ years beginning with the work of
Nel Caine [1]. Over time there have been strong
connections established between rainfall and shallow
landsliding [2]. Refining and honing this relationshiphave obvious societal impacts with regard to protecting
lives, critical infrastructure, and properties [3].
The Caine threshold [1] first established a landslide
triggering threshold for precipitation, over durations fromone minute to 90 days, based on a worldwide database of73 landslides for which rainfall data existed. Caine’s work
resulted in an envelope curve beyond which landslides
were expected to occur, and took the form of an IntensityDuration curve in the form:
I = 14.82D−0.39(1)Where I was rainfall intensity in mm/h and D wasrainfall duration in hours.remains a widely used approach.
However, it became obvious both that landslides wereoccurring at precipitation values below the threshold(false negatives) and that exceeding the threshold did notguarantee the occurrence of a landslide (false positives).
This spurred researchers to use of larger datasets to create
lower thresholds [4, 5, 6, 7] with limited success.
Attempts to create better thresholds using antecedentconditions have also been derived [8, 9, 10] and continue
today, but arguably make the thresholds more complex
without making them more accurate.

*Here, we present a well constrained probabilistic
relationship between rainfall intensity and landslides.
This relationship begins to quantify what the existing
thresholds represent and permits relatively simplecalculations regarding the potential impacts of different
intensity storms.

2 Methods
The Klanawa study area (Fig. 1) is part of the Vancouver
Island Ranges, comprised of glacially over-steepened
volcanic and plutonic mountains extending from sea level
to about 912 m. Precipitation at sea level is typicallybetween 2,900 and 3,100 mm annually following almost
exclusively as rain between October and March [11].
Further inland precipitation and percentage of snow
increases with elevation.
The study area is in various stages of logged, juvenileforest, second growth, and old growth forest depending onlogging history. Debris flows and shallow landslides arecommon [11].
A probabilistic relationship that can be deployedelsewhere requires a result that explains the likelihood ofa landslide at a given rainfall intensity and duration, overa unit area. We therefore required: (i) a complete rainfall
record for the area under investigation, and (ii) a complete
landslide inventory for the same, as time constrained aspossible.

Corresponding author: richard.guthrie@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, 03009 (2023)
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https://doi.org/10.1051/e3sconf/202341503009

2.2 Landslide Data
Planet Fusion data were used to collect and acquirelandslide occurrences in the study area over our period ofrecord. These data provide daily cloud-free orthorectified
imagery, at 3 m resolution. Landslides were discovered byrunning a change detection process between the first andlast images of approximately 1,500 images, separatinglandslides from other surface changes, and determining
the first and last definitive images that bracketed theobserved landslides (Fig. 3).

Fig. 1. The Klanawa 90,259 ha study area on the west coast of
Vancouver Island. Red dots indicate landslide locations.

2.1 Rainfall Data
The number of intensity-duration rainfall events (ID-areapairs) that did not trigger landslides at a particular area
will overwhelm those that did. Each data point contains
and ID-area pair and a landslide count (0, 1, 2, …n).
We collected 6-hour gridded rainfall (2.5 km2 grid)from the Canadian Surface Prediction Archive [12] for theperiod between Feb 02, 2018, and Jan 18, 2023. These
data were processed and up-sampled (interpolatedbetween points) to generate hourly gridded ID-area pairs
one ha in size (Fig. 2).
Altogether we generated more than 0.5 billion ID-area(1 ha) pairs for each of three durations (6-hours, 12-hours,and 24-hours). The 12-hour and 24-hour tests ran on amoving 6-hour window.

Fig. 3. Example landslide change detection between image setsfrom PlanetFusion.

Image quality varied dramatically across dates, whichmeant considerable persistent uncertainty about thepresence of landslides on transition images. Landslide
dates were constrained, on average, within a 65-day

Fig. 2. Up-sampled 1 ha resolution rainfall data.

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Table 1. Probability of landslides per unit area for different
durations and intensities

period and assumed to be a result of the most intense
rainfall (6-hour, 12-hour, or 24-hour) over that period.
Fifty landslides were identified between 2018 and2022. Landslide counts were assigned to the ID-area pairs
at their specific location and assigned a time based on themaximum intensity for that duration.
ID-area pairs were then grouped into 1 mm intensity
bins where each bin contained the total landslide countfrom about 0.54 billion possible ID-area pairs (theexposure time).
Probability was determined by dividing landslidecounts in each intensity bin by the exposure time.

3 Results
Probabilities were plotted for 6-hour, 12-hour, and 24hour. Here we graphically present the results for the 6hour for conservation of space (Fig. 4). The widelyreferenced Caine [1], Crosta and Frattini [5], Jakob andWeatherly [6] and Guzzetti et al. [4] thresholds are alsoplotted within the Fig. 4.

Future work is required by others to test the broader
applicability of these relationships. Broader applicability
may be subject to differences in land use, geology,regional climate, and bio-geomorphic regimes. Similar
approaches performed in post-wildfire scenarios indicate
shows a higher occurrence of debris flows whencompared to the relationships presented here.

Landslides are both possible and observed at lower
rainfall intensities (Table 1) but their probability ofoccurrence is much lower. The Caine threshold [1] resultsin about a one percent chance (0.01) of at least one
landslide per 100 km2 for the intensity-durations
measured here.

The findings show, for the first time, what publishedthresholds mean for a given storm. The relations
demonstrate that different size study areas produce a
different a likelihood of at least one debris flow is initiatedunder different rainfall intensities and durations.
Despite the recognition that the broader application ofthese relationships need to be determined, we neverthelessexpect these have broad applicability.

References

1.

N. Caine, Geografiska Annaler. Series A, PhysicalGeography 62, 1-2 (1980)

2.

F. Guzzetti, S. L. Gariano, S. Peruccacci, M. T.
Brunetti, M. Melillo, Rainfall and Landslide
Initiation, in Rainfall. Modeling, Measurement andApplications, Elsevier (2022)

3.

D. Petley, Geology 40, 10 (2012)

4.

F. Guzzetti, S. Peruccacci, M. Rossi, C.P. Stark,Landslides 5 (2008)

5.

G.B. Crosta, P. Frattini, Rainfall thresholds fortriggering soil slips and debris flow, in Proceedingsof the 2nd EGS Plinius Conference on
Mediterranean Storms, Siena (2001)

Fig. 4. Probability of landslides/ha by 6-hour rainfall intensity.

4 Discussion and Conclusions
The relationship between rainfall intensity and landslide
occurrence are robust. The correlation coefficients for all threecurves are strong (0.92, 0.99, and 1.0 for D6, D12, and D24
respectively) and we argue that the relations have highexplanatory power irrespective of duration and antecedentconditions.

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6.

M. Jakob, H. Weatherly, Geomorphology 54, 3-4(2003)

7.

M. T. Brunetti, S. Peruccacci, M. Rossi, S. Luciani,
D. Valigi, F. Guzzetti, Natural Hazards and EarthSystem Sciences 10 (2010)8.

M. Church, M.J. Miles, Meteorological antecedents
to debris flow in southwestern British Columbia;
Some case studies, in Debris Flows/Avalanches:
Process, Recognition, and Mitigation, The
Geological Society of America (1987)

9.

M.J. Crozier, Earth Surface
Landforms 24 (1999)

Processes and

10. G.F. Wieczorek, T. Glade, Climatic factors
influencing occurrence of debris flows, in Debrisflow Hazards and Related Phenomena, Berlin,Springer (2005)
11. T. Rollerson, D. Maynard, S. Higman, E. Ortmayr,
Klanawa landslide hazard mapping pilot project, inJoint Conference of IUFRO 3.06 Forest Operations
under Mountainous Conditions and the 12th
International Mountain Logging Conference, June
13-16, Vancouver (2004)
12. J. Mai, K. C. Kornelsen, B. A. Tolson, V. Fortin, N.
Gasset, D. Bouhemhem, D. Schafer, M. Leahy, F.
Anctil, P. Coulibaly, Bulletin of the American
Meteorological Society 101, 3 (2020)4