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Debris-flow risk-to-life: upper-bound preliminary screening
Tim Davies1*, Mark Bloomberg1, Dave Palmer2 and Tom Robinson1
1University of Canterbury, Private Bag 4800 Christchurch 8140, New Zealand2Scion, PO Box 29237, Riccarton, Christchurch 8440, New Zealand

Abstract. Where the potential for future debris-flow occurrence is unrecognised, developments can be
unknowingly exposed to debris-flow impact, with corresponding risks to lives. Debris-flow modelling isunsuited to routine local office use, so a simple screening procedure is proposed to enable local officials toidentify locations where debris flow risk-to-life may be unacceptable, and prioritise where expert modelling
and risk analysis are most urgently required for risk-management decision-making . This procedure
calculates catchment Melton ratio R from topographic data, uses a linear upper bound of field data relating
R to the annual probability of debris-flow occurrence, and matches a model-based debris-flow risk-to-life
analysis for Matatā, New Zealand. Our data suggest that any development exposed to debris flows will requirea detailed risk assessment to ensure that risk-to-life does not exceed acceptable levels.

1 Introduction
Debris flows are extreme events triggered in steep,
erodible catchments by intense rainfall causing highsediment inputs to streams. Debris flows differ fromnormal floods in material composition (a dense slurry offine sediment in water capable of transporting highconcentrations of coarse sediment), flow behaviour(multiple discrete surges with bouldery heads and finer,
less dense tails) and frequency (decadal or less in manycatchments). Thus, while debris-flow risk management
is often assumed to be similar to flood risk management,
it is fundamentally different [1].
Because debris flows occur infrequently in any
given watershed, many catchments susceptible to debris
flows have no historic records of their occurrence, so
their ability to generate debris flows may beunrecognised. Development of land in such areas meansthat assets might be vulnerable to debris-flow impact in
the future. Future deaths and damage can be avoided
only if debris-flow-susceptible areas can be identified
easily and reliably. Reconnaissance-level studies [2,3]suggest that significant developments currently occupy
areas in New Zealand that may be subject to debris-flowhazards. Recent studies [4] show that debris-flow riskto-life is a growing issue worldwide.
Over recent decades there has been a global movetowards management ofrisk (defined as event
probability x event consequence) as the key factor for
quantifying the impacts of natural hazards on society.
The 2015 Sendai Framework [5] focussed international
disaster management on disaster risk reduction, which
requires the ability to quantify risk, in turn requiring theability to identify hazards and quantify their potential fordamaging society.

To reduce future debris-flow disasters, it istherefore necessary to identify existing and proposeddevelopments located in debris-flow hazard areas and toquantify the corresponding risks. This ability is requiredby organisations responsible for land-use planning,particularly their in-house and/or external advisers innatural hazard risk, science and engineering. The present
work is aimed at such organisations and advisers,
particularly in regions where debris-flow risk ispresently poorly known, and people with limited skills
and time may need to assess large numbers ofcatchments.
The urgent and widespread need to routinely
identify debris-flow hazard zones and realisticallyconstrain their annual probabilities of occurrence isunlikely to be met by debris-flow modelling. This isbecause such modelling [6,7] requires detailed dataacquisition and analysis by a range of specialists, and isthus likely to be both lengthy and expensive. Our
purpose herein is to develop an easily-usable
methodology to meet this need, readily-available data.
Where developments exposed to debris-flows hazards
are thus identified, more sophisticated methods can beused to better quantify the risks and develop risk
management strategies for those specific locations.

2 Catchment characteristics
The primary requirement for debris flow occurrence is alarge volume of widely-graded sediment available fortransport. Thus debris flows usually occur in activelyeroding catchments with steep gradients, and we use acatchment steepness criterion to characterise acatchment’s ability to generate debris flows: the Meltonratio (R), defined as the catchment relief divided by thesquare root of the catchment area. Melton ratio analyses* Corresponding author: tim.davies@canterbury.ac.nz© 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/).

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can apply to a whole catchment or to catchment
segments bounded at their lowest point by selected
points in a stream network [8,9].
The Melton ratio has frequently been used toidentify catchments capable of generating debris flows[10 and references therein]. It has the advantage that R
can be computed on a regional basis using GIS withdigital elevation models of moderate precision [3], but
no association between R and debris-flow probability
has hitherto been established.

3 R and debris-flow evidence
Fig. 1 shows data relating R to the presence of evidence
of debris-flow occurrence for over 800 catchments in
Canada (upper) [11] and over 600 others worldwide(lower) [12]. Clear (but different) relationships can bederived in each case between R and the proportion p ofcatchments that show evidence of debris flows (Fig. 2).
A linear envelope (dashed line) denotes a conservative
estimate of the maximum value of p for given R for all
the data.

Fig. 2. Relationships between R and proportion ofcatchments with evidence of debris flows.

The significance of this relationship is the fact that
it is linear. Thus the relative R values of different
catchments 1 and 2 are proportional to their relative
maximum probabilities of generating debris flows
within time te. Further, if we assume that te is similar
between catchments, the relative R values also describe
their relative maximum likely annual probabilities pa:

4 Debris-flow frequency
However, the annual probability of debris-flow
occurrence in any given catchment remains unknown,.
Using the envelope relationship of Fig. 2,p ≤ 1.67R

pa1/pa2 = R1/R2(1)(2)

The quantity of data underlying Fig. 2 (about 1500
catchments in Europe, North America and NewZealand) suggest that the envelope relationship may beuniversal, at least in these regions. If so, any catchment
in these regions in which debris-flow probability has
been determined can serve as a calibration catchment.
Only a small number of catchments worldwide
have published data on the past occurrence of many
debris flows. Table 1 lists some of these catchments(volcano catchments excluded) along with their annual
probability of debris-flow occurrence pa and Melton ratio
R. It is notable that the instrumented catchments
generally have higher frequencies of debris-flow
occurrence than the non-instrumented catchments,
because they preferentially utilise catchments known toexperience frequent debris flows. Significantly, theupper bound of all data for non-instrumented catchments
is well-defined by the dashed line in Fig. 3:

in which p = pe is the maximum probability that acatchment with given R has produced a debris flow
within the (unknown) past time te that it takes for debrisflow evidence to be eliminated by fluvial and otherprocesses.

pamax ≈ 0.35R or pa ≤ 0.35R(3)which is linear and consistent with the expectation
deduced from Fig. 2. A much larger database would
obviously be useful in better defining this relationship,
but such data are rare. This kind of relationship, basedon empirical data, appears more realistic than thecommon strategy of selecting a critical R-value below
which it is (arbitrarily) assumed that debris flows neveroccur [2].

Fig. 1. Data from [11] (upper) and [12] (lower) relating
Melton Ratio R to evidence of debris-flow occurrence.

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Table 1: Melton (R) and annual frequency of debris flows(pa): non-instrumented and instrumented catchments.
Numbers in square brackets are references.

5 Risk calculation
Calculating risk for a given site (e.g. a small alluvial fan)requires knowledge of the impact a debris flow will haveon a development. Since we calculate pamax as the upperbound of the probability vs R relationship, we also use
the upper bound impact in calculating risk.
Consider a development with a population of 100 on
a fan whose catchment has R = 0.2. In this case themaximum risk-to-life is 0.35*0.2*100 = 7 deaths per
year maximum (dpym), assuming the greatest possible
impact (i.e anyone affected by a debris flow dies). If theoccupancy rate was 70% and occupancy time was 35%,
the risk would reduce to about 2 dpym. A further
reduction factor might be the proportion of the fan area
on which people are present - if this is 50%, then wecome down to 1 dpym. Fragility data for debris-flow
deaths within dwellings could reduce the dpy by afurther order of magnitude [25] to 0.1 dpym. In New
Zealand, the acceptable limit is 10-3 to 10-4 dpy [26], so
further investigation would be indicated in this case.
This example suggests that, for any catchment
known to be able to generate debris flows, risk-to-life islikely to be high enough to require detailed investigationof whether mitigation measures will be needed to reduce
the risk.

Non-instrumented catchments
Matatā (New Zealand) [13] R=0.17 pa=0.03=0.18R
Varuna (Switzerland) [14] R=0.9 pa=0.07=0.08R
Muleta (Switzerland) [15] R=1.0 pa=0.02= 0.02R
Chalance (France)[16] R=1.4 pa=0.06=0.05R
Ritigraben (Switz)[17] R=0.6 pa=0.13=0.20R
Bärenrüfe (Austria)[18] R=1.4 pa=0.13=0.09R
Cheekeye (Canada)* [19] R=0.4 pa=0.04=0.10R
V. di Gallo 1 (Italy) [20] R=1.13 pa=0.29=0.26R
V. di Gallo 2 (Italy) [20] R=1.14 pa=0.13=0.11R
V. di Gallo 3 (Italy) [20] R=0.84 pa=0.22=0.26R
V. di Gallo 4 (Italy) [20] R=1.16 pa=0.06=0.05R
V. di Gallo 5 (Italy) [20] R=0.31 pa=0.10=0.32R
V. di Gallo 6 (Italy) [20] R=1.32 pa=0.32=0.24R
V. di Gallo 7 (Italy) [20] R=0.77 pa=0.21=0.27R
V. di Gallo 8 (Italy) [20] R=1.36 pa=0.20=0.15R
V. di Gallo 9 (Italy) [20] R=0.57 pa=0.27=0.47R
Mean
R=0.90 pa=0.14=0.16R* Historical events only
Instrumented catchmentsSchipfenbach ( Switz) [21] R=1.4 pa=0.49=0.35R
Lattenbach (Austria)[22]

6 Example: Matatā, New Zealand

R=0.9 pa=0.26=0.28R

At Awatarariki fan, Matatā, North Island, New Zealand,
which has R = 0.17, a comprehensive risk analysis wascarried out following a destructive debris flow in 2005[30]. Using the present approach, the upper-bounddebris-flow probability would be calculated from (4) as
pamax = 0.35*0.17 = 0.06 per year (~ 17-year returnperiod; note that Table 1 gives pa = 0.03 from field data).
Applying our value of life-vulnerability in a building on
a fan impacted by a debris flow (0.1) to pamax (0.06) gives
a maximum individual risk to life (MIRTL) = 6*10-3 peryear for the Awatarariki fan, which is clearly
unacceptable. Thus our procedure indicates that debrisflow risk-to-life on the fan could be unacceptable, anddetailed risk analysis and management would be needed.
The risk analysis for Matatā [27] used a numericalmodel (RAMMS; [28]) calibrated on the volume,recurrence interval based on rainfall, and deposit extent
of the 2005 event. The model generated deposit extents
for a range of volumes, with corresponding probabilities
estimated from rainfall frequencies. This, together withscenario distributions of occupation and vulnerability,
yielded risk-to-life values on Awatarariki fan from 10-2
to 10-5, that led to planned retreat from the area as the
only realistic way to reduce the risk to acceptable levels[8]. The risk analysis for Matatā is consistent with thepresent analysis.

Illgraben (Switzerland) [21] R=0.6 pa=0.55=0.92R
Moscardo (Italy)[23]
Chalk Cliffs (USA)[21]
Reibaxader (Spain)[21]
Gadria (Austria)[21]
Shenmu (China)[21]
Ergou (China)[21]
Real (France)[21]
Jiangjia (China)**
[24]
Mean
** Not plotted in Fig. 3

R=0.57 pa=0.9=1.6R
R=1.1 pa >1.0>1.0R
R=1.6 pa=1.2=0.7R
R = 0.6 pa=1.0=1.4R
R=0.2 pa=1.0=4.0R
R=0.5 pa=4.0=8.0R
R=0.6 pa=1.0=1.6R
R=0.31 pa=11=35R
R=0.77 pa=2.5=3.2R

7 Discussion
The maximum individual risk to life MIRTL of a person
in a dwelling in the catchment deposition area isestimated asFig. 3 Data from Table 1. Triangles indicate non-instrumented
catchments, squares indicate instrumented catchments. The
dashed line is the approximate upper-bound envelope of noninstrumented catchment data (Eq. 3).

MIRTL = 0.1*pamax = 0.035R ≈ R/30

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If the acceptable risk level is < 10-3, then R needs to be <0.03 in order to indicate no need for detailed
investigation. This is conservatively low (the lowest R
associated with debris-flow evidence in Fig. 2 is 0.14) as
befits a screening analysis, and could be amended byexpert personnel in specific cases.

19. M. Jakob, P. Friele, Geomorphology 114(3), 382395 (2010)
20. M. Pelfini, M. Santilli, Geomorphology 101(4),721-730 (2008)
21. M. Hürlimann, D. Rickenmann, C. Graf, Canadian
Geotechnical Journal 40(1), 161-175 (2003)
22. J. Hübl, A. Schimmel, R. Koschuch, T. Yamada,
Evaluation of different methods for debris flow
velocity measurements at the Lattenbach Creek, inINTERPRAEVENT 2018 in the Pacific Rim
Symposium proceedings, pp 2-8 (2018).
23. L. Marchi, F. Cazorzi, M. Arattano, S. Cucchiaro,
M. Cavalli, S. Crema, Natural Hazards and EarthSystem Sciences 21(1), 87-97 (2021)
24. P. Cui, X. Chen, Y. Wang, K. Hu, Y. Li, Jiangjia
Ravine debris flows in south-western China,
in Debris-flow hazards and related
phenomena, Springer, Berlin, Heidelberg, 565-594(2005)
25. R. Bell, T. Glade, Natural Hazards and EarthSystem Sciences 4(1), 117-131 (2004)
26. T. Taig, C. Massey, T. Webb, Principles andcriteria for the assessment of risk from slope
instability in the Port Hills, Christchurch. GNS
Science Consultancy Report 2011/319 (2012).
27. Tonkin & Taylor Ltd. Supplementary risk
assessment debris flow hazard Matatā, Bay ofPlenty. Whakatane District Council, New Zealand
29115.2000 (2015)

References
1.
2.
3.

M. Jakob, P. Jordan, Canadian Journal of civilengineering 28(3), 425-439 (2001)
A.J. Welsh, T.R.H. Davies, Landslides 8(2),(2011).
M. Bloomberg, D. Palmer, Estimation ofcatchment susceptibility to debris flows and debris
floods–Marlborough Sounds, Pelorus Catchment
and Wairau Northbank, Draft Report toMarlborough District Council, 27p (2022)

4.

C.A. Dowling, P.M. Santi, Natural Hazards 71(1)(2014)
5. A. Aitsi-Selmi, S. Egawa, H. Sasaki, C. Wannous,
V. Murray, International Journal of Disaster Risk
Science 6(2), 164-176. (2015)
6. J. Farrell, T.R.H. Davies, Debris flow risk
management in practice: a New Zealand casestudy, in Assoc. Env. and Eng. Geol.; spec. publ. 28(2019)
7. M. Jakob, Environmental & Engineering
Geoscience 27(2), 153-166 (2021)
8. K. Holm, M. Jakob, E Scordo, An inventory andrisk-based prioritisation of Steep Creek Fans inAlberta, Canada, in E3S Web of Conferences, 7(2016)
9. M. Sturzenegger, K. Holm, C.A. Lau, M. Jakob,
Environmental and Engineering. Geoscience 27(2)(2021)
10. F.A. De Scally, I.F. Owens, Earth Surf. Proc.
Landforms 29 (2004).
11. M. Jakob, S. Davidson, G. Bullard, M. Busslinger,B. Collier-Pandya, P. Grover, C.A. Lau, WaterResources Research 58(4), (2022)
12. M. Bertrand, F. Liébault, H. Piégay, NaturalHazards 67(2) (2013)
13. M.J. McSaveney, R.D. Beetham, G.S. Leonard, The
18 May 2005 debris flow disaster at Matatā:
Causes and mitigation suggestions. GNS Science
Client Report, 71 (2005)
14. D. Rickenmann, M. Zimmermann,Geomorphology 8(2-3) (1993)
15. F. Baumann, K.F. Kaiser, Arctic, Antarctic, andAlpine Research 31(2), 128-134 (1999)
16. M.M. Helsen, P.J.M. Koop, H. Van Steijn, Earth
Surface Processes and Landforms 27(12), 12991307 (2002)
17. M. Stoffel, I. Lièvre, D. Conus, M.A. Grichting, H.
Raetzo, H.W. Gärtner, M. Monbaron, Arctic,Antarctic, and Alpine Research 37(3), 387-395(2005)
18. E. Procter, M. Stoffel, M. Schneuwly‐
Bollschweiler, M. Neumann, Earth Surface
Processes and Landforms 37(9), 913-922 (2012)

28. A. Simoni, M. Mammoliti, C. Graf, Performance of
2D debris flow simulation model RAMMS, in Annual
International Conference on Geological and EarthSciences GEOS (2012).

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