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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
895
DOI: 10.4408/IJEGE.2011-03.B-097
TOWARDS A FREQUENCY-MAGNITUDE RELATIONSHIP
FOR TORRENT EVENTS IN AUSTRIA
J
oHannes
HÜBL, s
ven
FUCHS, f
loRian
SITTER & R
einHold
TOTSCHNIG
(*)
(*)
University of Natural Resources and Life Sciences - Institute of Mountain Risk Engineering - Vienna, Austria
relationships to be used in hazard and risk assessment
and might also be used for estimates of possible conse-
quences of climate change in the Eastern Alps.
K
ey
words
: historic database, torrent events, debris flow,
frequency-magnitude relationship, process characterisation
INTRODUCTION
Mountain hazards pose a continuous threat in
areas such as the Austrian Alps, including snow ava-
lanches, landslides and floods. In an alpine context,
flooding processes occur mostly in relatively small
torrent catchments. Torrents are defined as constantly
or temporarily flowing watercourses with strongly
changing perennial or intermittent discharge and flow
conditions, originating within small catchment ar-
eas (a
ulitzky
, 1980; s
laymakeR
, 1988; onR, 2009).
Apart from debris flows, torrent events show a variety
of different flow characteristics including pure water
runoff, fluvial sediment transport and debris floods
1
(a
ulitzky
, 1980; C
osta
, 1984; H
unGR
et alii, 2001;
ONR, 2009). In order to mitigate such hazards, knowl-
edge on the general predisposition of a catchment to a
certain torrent process, referred to hereafter as domi-
nant process
, has to be gained. Moreover, information
on the frequency (J
akob
& b
ovis
, 1996) and magni-
1
Torrential debris floods are characterised by considerable
transport of coarse sediment (S
cheiDl
& r
icKeNmANN
, 2010). Hy-
perconcentrated flows are used as a synonym for debris floods
(c
oStA
, 1984; 1988) but in general transport larger amounts of
fine sediment in suspension (S
cheiDl
& r
icKeNmANN
, 2010)
ABSTRACT
Hazard assessment and the design of mitigation
measures against mountain hazards are usually based
on statistically derived magnitude-frequency relation-
ships of process parameters such as discharge, flow
velocity, or the volume of debris deposits. However,
with respect to debris flows there is a particular lack
of such data, as these processes are rare phenomena,
the systematic measurements of relevant parameters
have only been carried out in selected watersheds
within the last decades. In some areas, geomorphic
and stratigraphic assessments and dendrochronology
studies have been used for estimating magnitudes and
frequencies of debris flow events. However, there is
still an information gap for quantitative debris flow
hazard assessment based on recurrence intervals and
associated magnitudes. Our study aims to close this
gap by an analysis of an Austrian database of historic
events. Information on a local and regional scale has
been gathered from records of the Austrian Torrent and
Avalanche Control Service and the transcription of the
so-called “Brixner Chronicle” (s
tRele
, 1893). The ear-
liest events of our database date back to the 6th century,
while in-depth information on the events is available
since the 18
th
century. In total, more than 20,100 tor-
rent events were recorded, and around 5,700 have been
identified as debris flow-like events. We report how
to best identify different process types and to derive
quantitative information from historic texts. Our results
may improve the evaluation of frequency-magnitude
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J. HÜBL, S. FUCHS, F. SITTER & R. TOTSCHNIG
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METHODOLOGY
The database was derived from an analysis of
written reports which were compiled during the im-
plementation of hazard maps by the Austrian Torrent
and Avalanche Control Service (WLV)
2
. This data
source was completed by the transcription and analy-
sis of the “Brixner Chronicle” (s
tRele
, 1893). Table 1
summarises the hazard process groups and their sub-
categories (referred to as processes) that were includ-
ed in the database. As the sources of this database are
primarily focused on mountain hazards, flood events
related to lowland rivers are mostly excluded.
DATA ACQUISITION
Following the axiom of the “3W-Standard”, the
process group and the process, the name of the water-
shed and the corresponding geographical location, as
well as the date of the event were initially extracted
from the raw data and entered in the first form. Key-
words were used to define the allocation of the event
to a certain process type. The names of the watershed
and the affected villages were given in the event de-
scription for most datasets. Using a GIS environment,
a so-called information point including geographic
coordinates was assigned to each data record. The
structure of the database took the inhomogeneous for-
mat of the event dates into account (recent events of-
ten included information on the year, month and day,
and sometimes the time of day, while only the year
was recorded for mediaeval events).
Furthermore, where available, information on
both event magnitude and triggering factors were
gathered and stored in the database. If such informa-
tion was not available, qualitative indicators recorded
in the run-out area, e.g., spatial extent, number of
plots affected, or deposition heights were used as a
proxy to determine the event magnitude (Fig. 1). If no
corresponding information was provided in the event
description, a magnitude was not assigned in the indi-
vidual dataset (“magnitude not assessed”).
If available, additional information regarding
the meteorological triggering factors such as type
and amount of precipitation was included in the in-
dividual datasets.
A quality code was attached to the quantitative
2
The Austrian Torrent and Avalanche Control Service is a
federal institution operating throughout Austria to protect the
population from torrent hazards and other mountain hazards (r
e
-
PuBliK
Ö
Sterreich
, 1975).
tude (m
aRCHi
& d’a
Gostino
, 2004) of an event is a
compulsory prerequisite for any mitigation concept,
as well as hazard and risk assessment. Especially with
respect to vulnerability assessment of elements at risk,
generally seen as a central part in the framework of
risk assessment, information on the type of process and
the process magnitude and frequency is indispensable.
From an Austrian perspective, systematic measure-
ments of such parameters have been carried out only
in selected watersheds over the last decades. Only ap-
proximately 100 out of 10,000 torrent catchments are
equipped with monitoring devices. Such devices pro-
vide information on discharge used in the deduction of
frequency and magnitude. As measurement data from
smaller catchments is virtually not available at present,
alternative procedures to estimate frequency and mag-
nitude are necessary, e.g., stratigraphic methods (C
oe
et alii, 2003), dendrogeomorphic methods (J
akob
&
b
ovis
, 1996; m
ayeR
i., 2010) and lichenometric meth-
ods (H
elsen
et alii, 2002). These methods are tradi-
tionally conducted by earth scientists to assess land-
slide occurrence, while in contrast, historical databases
are used by local administrative bodies to estimate the
impact of natural hazards (C
aRRaRa
et alii, 2003).
This study is based on a dataset of historic events
that was compiled at the Institute of Mountain Risk
Engineering (H
übl
et alii, 2010) on behalf of the
Austrian Federal Ministry of Agriculture, Forestry,
Environment and Water Management. First results
concerning the assignment of dominant process types
in torrent catchments and the estimation of mean fre-
quencies for selected catchments are presented.
Tab. 1 - Classification of processes (modified after DIS-
ALP, 2007)
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TOWARDS A FREQUENCY-MAGNITUDE RELATIONSHIP FOR TORRENT EVENTS IN AUSTRIA
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
897
SPATIAL DISTRIBUTION ANALYSIS
Using the geographic coordinates of the informa-
tion points, the spatial distribution of torrent events in
Austria was visualised. Firstly, the number of fluvial
and debris flow-like events per individual catchment
was summed up, and the relative share of process cat-
egories was calculated. If, during the set of calcula-
tion, more than 60% of the entire number of events
within an individual catchment was characterised by
being either fluvial-like or debris flow-like, a cor-
responding dominant process was assigned to the
respective catchment. If the proportion was between
40% and 60%, no dominant process was derived and
the corresponding catchment was classified as inter-
mediate. Secondly, the resulting dominant processes
were assigned to the area of individual catchments, re-
sulting in a threshold size for the occurrence of debris
flow-like events.
In a further step, the catchment layer was inter-
sected with the geologic map of bedrock (e
GGeR
et
alii, 1999) to obtain a relation between lithology and
the occurrence of dominant torrent processes. There-
by, a lower threshold of 60% by area of a specific
type of bedrock was defined for the assignment of a
dominant geological unit to a catchment otherwise a
catchment was classified as intermediate. Combin-
ing the information regarding dominant processes
and dominant geological units on a catchment basis,
the specific occurrence of processes in relation to a
specific type of bedrock was assessed.
information entered in the database to define the un-
certainty inherent to this information. The following
codes were used: measurement, estimation, unclear
information, not determinable.
Applying the second form of the data acquisition
tool, existing information on damage and losses was
entered into the database. As far as quantitative infor-
mation was available, the entry form provided five
categories of losses, as shown in Tab. 2. For damages
related to the built environment, different damage lev-
els, i.e. destroyed, damaged, and/or (in case of linear
infrastructures) interrupted, were selectable.
DATA ANALYSES
The datasets were analysed in order to achieve
spatial and temporal process patterns on a catch-
ment scale. As the main focus of this paper was de-
bris flow-like processes, fluvial-like datasets were,
apart from comparative purposes, not included in the
subsequently described analyses. Debris flow-like
process include an aggregation of debris flows and
debris floods due to the general understanding of de-
bris floods as a transition between fluvial sediment
transport processes and debris flows (C
osta
, 1988).
Events characterised by pure water runoff or fluvial
sediment transport were aggregated as fluvial-like
events. Within the category of debris flow-like proc-
esses approximately 5,700 datasets were available
for further analysis, i.e., a spatial distribution analy-
sis and a time series analysis.
Tab. 2 - Categories and subcategories for recording losses
Fig. 1 - Classification of process magnitudes, applicable
for torrent events in European mountain regions
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
tribution of datasets across different process groups
and the dominance of flooding processes (including
torrent events) is evident.
In Figure 3 the relative distribution of hydrologic
processes is presented. Focusing on these hydrologic
processes, 14,400 or 71% of the datasets can be at-
tributed to fluvial-like events (pure water runoff and
fluvial sediment transport) and 5,700 or 29% of the
datasets can be attributed to debris flow-like events
(debris flood and debris flow).
In Figure 4 a time series of debris flow-like events
is shown for the period between 1880 and 2010.
The time is plotted on the abscissa and the number
of events is plotted on the ordinate. The number of
events per year is shown by black bars and the number
of events per decade is presented by grey bars. The
annual mean is equal to 37 events. The data shows a
slightly increasing trend for debris flow-like processes
over the entire period, whereas the number of events
seems to decrease sharply from the 1960s onward.
The number of events per year as well as per
decade reaches a maximum in the 1950s, 1960s and
1970s. A considerable above-average number of
events was observed in 1959, 1965, 1966 and 1975.
In Figure 5 the results of the assignment of domi-
nant process types to individual torrent catchments
is shown. The individual catchments were assigned
to either debris flow-like, flood-like or intermediate
process types. A concentration of torrent catchments
prone to debris flow-like processes is visible for the
Western part of Austria (Provinces of Tyrol and Vorar-
lberg) and for the district of Bruck an der Mur (Prov-
ince of Styria). Based on the assignment of dominant
process types to catchment areas, a certain threshold
of catchment area size was found for the distinction
between catchments prone to debris flow-like proc-
esses and those catchments that do not show specific
process proneness. Debris flow-like processes were
observed only in catchments < 80 km
2
, whereas 95 %
of all catchments showing a dominance of debris
flow-like process are smaller than 15 km
2
(Tab. 4).
In addition to the dominant process, the prevail-
ing geological unit within individual catchments, dis-
TIME SERIES ANALYSIS
Apart from an overall time series for all events
highlighting the number of events per year and decade,
times series for two individual torrents were derived
for a more detailed analysis with respect to event mag-
nitude. The torrent Bretterwandbach and the torrent
Farstrinne were chosen due to their long series of well-
documented events. The location of these torrents is
illustrated in Fig. 2. The torrent Bretterwandbach is lo-
cated in Western Austria close to the village of Matrei
in Osttirol. The west-exposed basin is part of the
Granatspitzgruppe mountain range with an elevation
difference between 938 m and 3,085 m a.s.l. The catch-
ment covers an area of 18.2 km
2
. Lithologically, the ba-
sin comprises mainly the Penninic unit and crystalline
rock. The Farstrinne is located in Western Austria close
to the village of Umhausen. The basin is south-west
exposed and extends over an area of about 5.8 km
2
be-
tween 944 m and 3,010 m a.s.l. Crystalline rock is the
predominating lithological unit in this catchment.
Using the two time series, the mean frequency
(return period) of both ordinary and extraordinary
events was calculated. Ordinary events were defined
as those events with either a small or a medium mag-
nitude, whereas extraordinary events were aggregated
from large and very large events (compare Fig. 1). The
mean recurrence interval was calculated as a ratio be-
tween the period of records (time period between the
first recorded event and the present) and the number of
events of a certain magnitude that occurred during this
period of record (C
oe
et alii, 2003).
RESULTS
In total the database consists of 27,912 individual
datasets of different hazard type that occurred between
the 6th century and 2009. Table 3 summarises the dis-
Fig. 2 - Location of the test sites in the Austrian Alps, indi-
cated by arrows
Tab. 3 - Distribution of datasets
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TOWARDS A FREQUENCY-MAGNITUDE RELATIONSHIP FOR TORRENT EVENTS IN AUSTRIA
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
899
DISCUSSION AND CONCLUSION
A database of historic events, which included dif-
ferent hazards such as avalanches, slides, falls and
floods, was compiled for the Republic of Austria.
Information on a local and regional scale had been
gathered from records of the Austrian Torrent and
Avalanche Control Service and the transcription of
the so-called “Brixner Chronicle” (s
tRele
, 1893). Ap-
proximately 28,000 events, distributed over the entire
country, were entered into the database and subse-
quently analysed with respect to magnitude and fre-
quency. The earliest events of this database date back
to the 6th century, while in-depth information on the
events is available since the 18
th
century. More than
20,100 torrent events, including around 5,700 events
identified as debris flow-like, and 5,045 as debris
flows, represent the majority of the datasets. Three
data entries, defining the type of process, the date of
occurrence and the geographic location, were manda-
tory for each dataset and referred to as “3W-Standard”
(DIS-ALP, 2007). If available, additional information
regarding event magnitude, triggering factors and
regarding the quaternary deposits, was determined. In
Table 5 the number of catchments showing a specific
type of bedrock is summarised with respect to fluvial-
like and debris flow-like processes. Whereas the over-
all dominance of fluvial-like processes is obvious for
all types of lithology, the relative share of debris flow-
like processes in Chrystalline and Penninic areas and
regions characterised by Palaeozoic bedrock is larger
than in areas characterised by other geological units.
With respect to the large-scale analysis of individ-
ual catchments, a continuous time series of debris flow-
like events of two individual torrents, Bretterwandbach
and Farstrinne, is shown in Figures 6a and 6b. The
time is plotted on the abscissa and the magnitude of the
events is plotted on the ordinate. The process magni-
tude is classified into five classes: XL = very large, L =
large, M = medium, S = small, and na = magnitude not
assessed. The same period of time (1700 – 2010) is vis-
ualised in Figures 6a and 6b to improve the compara-
bility of the two time series, although the first recorded
event in the torrent Bretterwandbach already occurred
in the year 1445 and four events occurred before 1700.
In general, the majority of events are characterised by
small to medium process intensity. A concentration of
events can be observed in both figures around the sec-
ond half of the 19
th
century.
The calculated return periods based on these time
series are given in Table 6, combining events of the
XL- and L-type to a class of extraordinary events and
events of the M- and S-type to a class of ordinary
events. Within the period of records, the average prob-
ability of occurrence of M- and S-type events equals
1 in 26 years (Bretterwandbach) and 1 in 10 years
(Farstrinne), while the average probability of occur-
rence of XL- and L-type events equals to 1 in 56 years
and 1 in 26 years, respectively.
Fig. 3 - Distribution of datasets
Fig. 4 - Time series of debris flow-like events
Fig. 5 - Dominant process fortorrentc catchmens in aus-
tria
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
losses was included. Focusing on debris flow-like
events, a spatial distribution analysis and a time series
analysis was conducted to show the applicability of
such a database for an evaluation of frequency-magni-
tude relationships, and in particular with respect to the
framework of hazard and risk assessment.
The time series analysis showed that a maximum
of events occurred during the decades of 1950-1970,
while for individual years (particularly 1965 and 1966)
a prominent peak in the number of events was observed.
The spatial distribution analysis resulted in con-
siderable insights into the geographical distribution of
torrent events in the Austrian Alps. An above-average
concentration of debris flow-like processes is traceable
for the Western part of the Republic of Austria. These
processes are the evident and documented dominant
processes in the central part of the (populated) tor-
rent fans, assigned to the individual datasets and now
summed up for this analysis. This method is in line
with the understanding that the dominant process in
the central part of the deposition zone is used to define
the entire event characteristics (H
unGR
et alii, 2001).
Based on this assignment of dominant process
types to catchment areas, a certain threshold of catch-
ment area size was found for catchments prone to de-
bris flow-like processes. This threshold of catchment
area was 15 km
2
, and is in the same order of mag-
nitude as reported for European Alps in other studies
(e.g., 20 km
2
, m
aRCHi
& d’a
Gostino
(2004), 20-30
km
2
, m
aRCHi
& b
RoCHot
(2000) and 22 km
2
, R
iCken
-
mann
& z
immeRmann
(1993)).
An assessment of process type with respect to the
underlying geologic conditions was undertaken, and
resulted in a distinct relationship between different
geological units and the dominance of certain proc-
ess types. Whereas certain geologic units such as the
Bhoemian Massif, the Molasse Zone and the Rheno-
Danubian Flysch Zone show only a small number of
catchments prone to debris flow-like processes, the
relative share of debris flow-like processes in Chrys-
talline and Penninic areas and regions characterised
by Palaeozoic bedrock is clearly above average.
An in-depth assessment of magnitude and fre-
quency of debris flow-like events was carried out for
two study sites in Western Austria. Due to the data
quality, a semi-quantitative assessment of magnitude-
frequency relationships was established. The results
showed that the probability of occurrence of events of
smaller magnitude (ordinary events) is between 1 in
10 and 1 in 26 years, while events of larger magnitude
(extraordinary events) occur rarer with a frequency of
up to 1 in 56 years.
In general the analysis of the database provided
valuable insights with respect to process patterns in
mountain environments. However, the analysis also
showed some limitations due to an incomplete or miss-
ing documentation of events. Thereby, an increase in
data reliability was traceable for more recent events,
while older entries in general were more qualitative
in terms of event magnitude. The documentation of
events was mainly fragmentary in areas where human
structures were missing, a phenomena also observed
Tab. 4 - Threshold of catchment area for different proc-
esses
Tab. 5 - Number of catchments with dominant processes
in geological units; the number gives the absolute
value for individual process types while the per-
centage indicates the relative share between proc-
ess types
Tab. 6. - Return periods for the torrents Bretterwandbach
and Farstrinne
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TOWARDS A FREQUENCY-MAGNITUDE RELATIONSHIP FOR TORRENT EVENTS IN AUSTRIA
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901
Especially with respect to alpine torrent process-
es (but principally also with respect to other moun-
tain hazards such as snow avalanches) the major
problem related to the establishment of frequency-
magnitude relationships is the inherent complexity
of the system. Moreover, the relationship between
magnitude and frequency of an event in a certain
(monitored) catchment is not necessarily transferable
to an adjacent catchment that is not monitored due to
possible changes in initial and boundary conditions.
However, even if individual catchment properties
may be responsible for individual process character-
istics, general conclusions on process characteristics
can be drawn. Nonetheless, the established relation-
ship between process magnitude and frequency is
only an approximation, and has to be evaluated care-
fully with respect to possible sources of (aleatory and
epistemic) uncertainty.
ACKNOWLEDGEMENTS
This work was supported by the Austrian Federal
Ministry of Agriculture, Forestry, Environment and
Water Management and the Austrian Science Fund
(Contract L535-N10).
in other studies (J
aediCke
et alii, 2009). However, this
implies that the dataset is relatively reliable in areas of
anthropogenic activity, such as settlements or trans-
portation corridors.
Despite these limitations, the analysis of process
magnitude and frequency as well as the assignment
of dominant process types to individual torrent catch-
ments is of high value for the assessment of hazard and
risk, i.e., for the implementation of technical protection
measures and the assessment of vulnerability (f
uCHs
,
2009). In order to allow for a comparison of risk re-
duction as a result of the implementation of different
protection alternatives (H
olub
& H
übl
, 2008; H
olub
& f
uCHs
, 2009), and the resulting shift in vulnerability
of elements at risk and the society, information on the
magnitude and frequency of events is indispensable.
Dealing with physical vulnerability, also the type of
process affects the vulnerability of elements at risk
and, hence information about it is a compulsory pre-
requisite for vulnerability assessment. In this context
various vulnerability functions were developed for dif-
ferent torrent processes (e.g., f
uCHs
et alii, 2007 and
a
kbas
et alii, 2009; for debris flows and t
otsCHniG
et
alii (in press) for fluvial sediment transport).
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