NHESSNatural Hazards and Earth System ScienceNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus GmbHGöttingen, Germany10.5194/nhess-15-985-2015Roads at risk: traffic detours from debris flows in southern NorwayMeyerN. K.nelekristin@gmail.comSchwanghartW.https://orcid.org/0000-0001-6907-6474KorupO.NadimF.International Centre for Geohazards (ICG) c/o NGI, Oslo, NorwayUniversity of Oslo, Department for Geosciences, Oslo, NorwayUniversity of Potsdam, Institute of Earth and Environmental Science, Potsdam, GermanyNorwegian Geotechnical Institute (NGI), Oslo, NorwayN. K. Meyer (nelekristin@gmail.com)19May201515598599523September201430October2014–1February2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.nat-hazards-earth-syst-sci.net/15/985/2015/nhess-15-985-2015.htmlThe full text article is available as a PDF file from https://www.nat-hazards-earth-syst-sci.net/15/985/2015/nhess-15-985-2015.pdf
Globalisation and interregional exchange of people, goods, and services has
boosted the importance of and reliance on all kinds of transport networks.
The linear structure of road networks is especially sensitive to natural
hazards. In southern Norway, steep topography and extreme weather events
promote frequent traffic disruption caused by debris flows. Topographic
susceptibility and trigger frequency maps serve as input into a hazard
appraisal at the scale of first-order catchments to quantify the impact of
debris flows on the road network in terms of a failure likelihood of each
link connecting two network vertices, e.g. road junctions. We compute total
additional traffic loads as a function of traffic volume and excess
distance, i.e. the extra length of an alternative path connecting two
previously disrupted network vertices using a shortest-path algorithm. Our
risk metric of link failure is the total additional annual traffic load,
expressed as vehicle kilometres, because of debris-flow-related road
closures. We present two scenarios demonstrating the impact of debris flows
on the road network and quantify the associated path-failure likelihood
between major cities in southern Norway. The scenarios indicate that major
routes crossing the central and north-western part of the study area are
associated with high link-failure risk. Yet options for detours on major
routes are manifold and incur only little additional costs provided that
drivers are sufficiently well informed about road closures. Our risk
estimates may be of importance to road network managers and transport
companies relying on speedy delivery of services and goods.
Introduction
Society's reliance on transport networks has grown extensively,
commensurately amplifying potentially adverse consequences of network
malfunction (Taylor and D'Este, 2003; Demšar et al., 2008; Andrey,
2010). Linear infrastructures such as road and rail networks, pipelines, and
power grids are sensitive to catastrophic disruption (Schulz, 2007). Such
network failure can be caused by, among others, vehicle accidents,
construction work, natural hazards, and terrorism (Tacnet et al., 2012).
These incidents can result in reductions or interruptions in
serviceability and thus determine the reliability of a network (Berdica,
2002). Transport network reliability is the degree of certainty with which
travel between A and B within the time period t is possible (Immers et al.,
2004); reliability is a function of the likelihood that an incident will
cause network malfunctioning and is determined by the likelihood of the
incidence itself and the robustness of the network against failure (Murray
and Grubesic, 2007). Network vulnerability analyses relate this likelihood
of failure to its economic and societal consequences (Jenelius, 2009). Most
road network analyses are concerned with urban networks where traffic
interruption often leads to congestion affecting a large number of people
(Taylor and D'Este, 2003; Appert and Chapelon, 2013). However, in
mountainous areas traffic disruption due to natural hazards such as
landslides may also present a threat to human life and cause significant delays,
reduced accessibility, and high economic costs (Scott et al., 2006). Recent
statistics suggest that ∼ 45 000 km of road and railways are
exposed to landsliding worldwide (Dilley, 2005). Hence, there is increasing
demand for quantitative studies that assess the transport network analyses
on interregional and national scales (Taylor et al., 2006).
In this study we focus on quantifying the risk of traffic network downtimes
caused by natural hazards and draw on the example of major roads in Norway.
The following case illustrates the need for appraising the consequences of
road closure: a flash flood in July 2006 washed away 30 m of the highway E14
that connects Östersund in Sweden and Trondheim in Norway and sustains
daily traffic of 1000–2000 vehicles/day. The shortest detour between both
ends of the washed out road section was > 200 km; partial
reopening of the road took 12 days. The estimated costs of repair were
EUR 1.2 million (Jenelius, 2010). Yet this assessment failed to
allocate costs for additional travel time and fuel consumption required to
circumnavigate the closed road. A calculation that assumes an average fuel
consumption of 6 L/100 km and a fuel price of EUR 1.5 L-1 would incur
additional costs of between 216 000 and EUR 432 000, or up
to 45 % of the structural damage. This simplified calculation merely takes
addition fuel consumption into account and illustrates important costs often
neglected in assessing road damage and calls for further enquiry. Moreover,
other costs related to work time loss and/or delays in delivery (especially
perishables) are not considered. These may add even higher additional costs
than computed for fuel consumption.
Study area and road network connecting major cities in southern
Norway. All traffic data were provided by the Norwegian Public Road
Administration Statens Vegvesen. Road characterisation and regions delineated by white
boundaries correspond to Norwegian nomenclature.
Norway's steep topography and high frequency of extreme weather events
expose a large portion of its transport infrastructure to natural hazards
(Bargel et al., 2011; Bjordal and Helle, 2011; Norem and Sandersen, 2012).
Norway is a large and sparsely populated country, and roads crossing remote
parts are often the only connection between larger cities (Fig. 1). Hence,
unanticipated detours often involve long additional distances. Moreover, the
demand for road serviceability has increased notably in the last decades.
The total annual person transport carried out by private cars in Norway had
doubled to ∼ 80 % by 2002 as compared to 1960. During the
same period, the volume of transported goods increased 9-fold and
remains the dominant mode of land transport in Norway (Boge, 2006). Mountain
valley floors collect most of the incoming natural water and sediment
fluxes. Roads located in such valleys are often affected by rapid mass
movements that degrade roads and interrupt traffic flow (Winter et al.,
2008). While rockfalls and snow avalanches are most frequent disturbances,
the rarer debris flows were responsible for the majority of all pavement
damages related to mass wasting from 2006 to 2009 (Bjordal and Helle, 2011).
Even though this study quantified structural damages to road infrastructure
from natural hazards, we are not aware of any analysis of the overall
functional value of the road network in Norway.
Here our aim is to merge graph theory and quantitative risk assessment to
quantify the functional impact of debris flows in terms of road closure and
associated risks for the south Norwegian road network (Fig. 1). We use a
two-step approach. First, we gauge the likelihood of debris-flow occurrence
in first-order catchments to determine, on a statistical basis, how frequently
roads need to be shut down in consequence. Second, we estimate the
functional value of the roads rather than their structural damage. We
express this functional value as the calculated total additional traffic
load resulting from road closures and assess the ensuing risk in terms of
total excess road kilometres per year. We conclude by highlighting potential
network weaknesses tied to two different debris-flow scenarios.
(a) Topographic susceptibility, i.e. aggregated probability of
debris-flow occurrence, in first-order catchments; (b) annual trigger
frequency in first-order catchments; (c) average traffic volume per day.
Data
With an area of ∼ 320 000 km2 mainland Norway extends
over nearly 1800 km in a north–south direction (57∘57′ N to
71∘11′ N). About 30 % of the country features mountainous areas
with steep slopes and harsh climatic conditions (Fischer et al., 2012). The
annual precipitation may exceed 4000 mm on the west coast, and the annual
mean temperature ranges between -8 ∘C in northern and central
southern Norway and +8 ∘C along the southern coast (Dyrrdal et
al., 2012). We focus on the area south of 64∘ N, which covers the
four regions of Vestlandet, Sørlandet, Østlandet, and Midt-Norge (Fig. 1).
Several mountain regions form a major divide between Vestlandet and
Østlandet, promoting maritime and continental climates respectively.
Our analysis covers > 40 000 km of road network. Europavegs are
the main arterial roads that connect the different regions, whereas Riksvegs
and Fylkevegs are regional and local roads respectively (Fig. 1). We
disregarded smaller urban roads not contributing to the regional or
interregional connectivity. Norwegian roads have a maximum speed limit of
80–100 km h-1 and usually consist of one track in each direction but are
multi-tracked close to the main cities. In more densely populated areas and
along the coast the network density is high, while the mountainous area in
the central part of the study area has a thin road network.
Our analysis draws from previous work on a topographic susceptibility model
for debris-flow source areas (Meyer et al., 2014) and a threshold model
specifying hydro-meteorological conditions needed to trigger debris flows
(Meyer et al., 2012). Both models are calibrated and validated with a
national mass-movement database featuring > 500 debris-flow
events recorded between 1979 and 2008 (http://www.skrednett.no/; Jaedicke et
al., 2009; Meyer et al., 2012, 2014). The topographic
susceptibility is based on a weights-of-evidence model using the two
topographic parameters of slope and flow accumulation with a resolution of
25 m × 25 m. This model identifies potential debris-flow source areas and
assigns spatial probabilities to each grid cell. Susceptibility to
debris-flow initiation is high where steep slopes
(∼ 20 to ∼ 60∘) and contributing areas of
∼ 0.02 to 2 km2 combine, i.e. mainly in the fjord
landscape along the west coast.
Trigger frequencies rely on an intensity–duration threshold derived from
past hydro-meteorological conditions (Meyer et al., 2012). In Norway, such
critical hydro-meteorological conditions are usually tied to heavy rainfall
and intense snow melt. Thresholds are ranked (minimum, medium, and maximum)
at 1 km × 1 km resolution and normalised by the precipitation day normal to
account for differences in the climatic regime. We use the diurnal medium
threshold and calculate the mean annual trigger frequency for the period
1981–2010 (Meyer et al., 2012).
For this study, we spatially aggregated the gridded data on topographic
susceptibility and annual trigger probability within first-order catchments
(http://atlas.nve.no; Fig. 2a, b). First-order catchments are the smallest
hydrometric reference areas in the officially used national catchment
database REGINE and have a median area of 8.5 km2. We
multiplied the fraction of terrain susceptible to debris flows with the
associated probability of occurrence for each first-order catchment. The
topographic susceptibility is highest in Vestlandet but decreases to the
east with lower topographic relief (Fig. 2a). We spatially averaged the
annual trigger frequency of all pixels within each catchment. Trigger
frequencies are highest on the plateaus between Vestlandet and Østlandet
and may reach more than seven triggering events per year (Fig. 2b).
We assess the daily traffic volume per road from data by the Norwegian
Public Road Administration Statens Vegvesen (Fig. 2c). Traffic volumes are high in urban
areas and along the coast where the population density is highest. There,
route sections are frequented commonly by > 10 000 cars/day.
Around Oslo, the capital and largest city of Norway, average traffic per day
exceeds 50 000 cars/day, whereas the mountainous core of the study area has
much lower volumes (< 2500 cars/day). Data on traffic volumes are
available for ∼ 93 % of the studied roads.
Example of a road network including terms used in this study.
MethodsGraph theory
We use graph theory for quantifying likely impacts of debris flows on
Norway's road network. In the following we briefly review some basic
terminology, algorithms, and assumptions pertinent to our application of
graph theory and road networks. For a more detailed introduction into graph
theory we refer to Gross and Yellen (2005) and Heckmann et al. (2015). A
graph G(VE) is the mathematical representation of a network defined by two
disjoint sets of vertices V and links E. A link is defined by two
vertices u and v, and two vertices are adjacent to each other when a
link {u,v} connects them. The topology of a graph is stored in an
adjacency matrix with n rows and n columns, where n is the number of
vertices in the network. An element in row u and column v in the
adjacency matrix is unity if there is a link between u and v; otherwise
the element is zero. We make the simplifying assumption that all links can
be traversed in both directions. Hence, our road network is an undirected
graph and the associated adjacency matrix is symmetric with respect to the
main diagonal. Vertices represent either road junctions or dead ends and
thus have 1, 3, or more incident links (or vertex degrees). We deviate from
this definition in cases where two or more distinct roads share the same
pair of nodes by introducing two-degree dummy vertices (Fig. 3). When
calculating the adjacency matrix of the road network, these dummy vertices
avoid the collapse of two or more links into a single link. We furthermore did not
include any loops, i.e. links with both ends sharing the same vertex.
Each road link has metric attributes such as length and traffic volume that
we used as weights in a shortest-path calculation. A path or route is a
sequence of vertices connected by links with no vertex being visited more
than once (Demšar et al., 2008). An origin vertex is connected with a
destination vertex if there is a path between them (Fig. 3). The shortest
path is the route between two vertices that minimizes the sum of weights. We
assume that all motorists choose the path with the shortest total travel
distance between two road junctions. Reorganisation of a shortest path
between two vertices is required if a link fails due to debris-flow impact
and subsequent road closure (Fig. 3). We assume that if this were the case
for a link belonging to the shortest path, motorists would use the shortest
alternative route. Thus, our simulation emulates the functioning of vehicle
navigation systems that in fact rely on a similar set of graph theoretic
algorithms. We refer to excess distance as the difference between the
shortest detour path and the original distance along a blocked road link. We
compute excess distance for each link in the road network by setting the
respective element in the distance matrix to zero and then reassessing the
shortest alternative path. The distance matrix resembles the adjacency
matrix, but its non-zero elements contain the travel distance between two
adjacent vertices. Excess distance is a local measure expressing the length
of detour between two adjacent vertices, whereas the total detour around a
blocked road may be lower if the distance between origin and destination
allows for more optimal alternative routes (Fig. 3). We focus on the road
network connecting the seven major cities in southern Norway, i.e. Oslo,
Lillehammer, Trondheim, Ålesund, Bergen, Stavanger, and Kristiansand. We
used MATLAB version R2012a (The MathWorks, 2012) and
MatlabBGL, a toolbox that interfaces with the Boost Graph Library (Siek et
al., 2001) for our network analysis, and Dijkstra's algorithm to compute the
shortest paths.
Flow chart showing aggregation and processing of data on different
scales: pixel, catchment, link, and path. For detailed description of
aggregation process see text.
Risk framework
We assess the probability and consequences of link failure within the risk
framework. In its most general form, risk R can be defined as R=H×C,
where H is the probability of a threatening event (hazard), and C
are the consequences related to H. The consequences C are a product of
the value of the elements at risk E and their vulnerability V such
that the risk equation becomes R=H× E ×V. Vulnerability V is a
factor between 0 and 1, indicating the severity of expected loss given a
hazard H, and expressed as a fraction of the total value of E. In the
context of network vulnerability, monetary values of road segments (pavement,
side rails, etc.) can be included to refer to the structural vulnerability
of the elements at risk. Hazard H may express the probability of
occurrence of a potentially damaging phenomenon within a given time period
and area (Downing et al., 2001). We approximate H by computing the
likelihood of debris-flow occurrence (Fig. 4) as the product of the
topographical susceptibility (Meyer et al., 2014) and the annual trigger
frequency for each first-order catchment (Meyer et al., 2012). We did not
convert this likelihood to a normalised probability in order to preserve
information about the annual triggering frequency. In any case, the shape of
the probability distribution of H remains the same. We then assigned the
likelihood of debris-flow occurrence in each catchment to the adjacent road
links. In cases where a road link intersected with more than one first-order
catchment, we used the sum of topographical susceptibilities times the
highest trigger frequency along the respective road link (Fig. 4). Thus,
derived link-failure likelihoods reflect the assumption that debris flows
occurring in small mountain catchments reach and take out the road for 1
day eventually. Hence, we assume a link vulnerability of unity. This is a
strongly simplified assumption as not all debris flows in these catchments
will cause equal damages on roads and may be subject to different closure
times accordingly. However, besides practical reasons this assumption seems
reasonable given that our analysis is based on debris flows that had
impacted roads in the past. We set the likelihood to zero for ferry
connections and tunnels longer than 1 km as we assume these reaches are
safe from debris-flow impact. However, we do not consider existing
mitigation measures that protect roads from the impact of debris flows. We
note that our use of link-failure likelihood is equivalent to the complement
of link reliability, a term commonly used in transport network analysis
(Murray and Grubesic, 2007; Boge, 2006). We preferred the term likelihood to keep
the term consistent with related measures on catchment and path level used
in our analysis (Fig. 4).
Our attention is on expenditures in terms of additional traffic loads
resulting from road closures and thus the functional value of the network
links. The product of traffic volume (vehicles/day), excess distance (km),
and closure time (days) gives the total additional average traffic load per
road closure (vehicles × km) (Fig. 4). Assuming that characteristic
closure times amount to 1 day, we multiply link-failure likelihood (1 year-1)
with additional traffic load to obtain the annual debris-flow-related link
risk (vehicles × km year-1) (Fig. 3). We explore the applicability of
this approach in two scenarios. The simpler scenario involves road closure
and subsequent traffic diversion by a single debris flow. An alternative
scenario is informed by the historical mass-movement database
(http://www.skrednett.no/; Jaedicke et al., 2009). This inventory indicates
that extreme weather events often trigger multiple debris flows; 667
documented debris flows were associated with 285 triggering events such that
one rainfall or snow-melt event triggered more than two debris flows in
average.
Excess distances resulting from potential road closures.
(a) Link-failure likelihood and (b) total additional traffic load
per road closure; main routes between seven large cities in southern Norway
are marked in yellow.
Matrix of distances on main routes (km) between major cities (lower
left) and the associated total path-failure likelihood (event/year) (upper
right); cells are highlighted in bold according to quartile-based classification of
failure likelihood.
Our network analysis shows that computed excess distances are longest
(> 200 km) through the central part of the study area (Fig. 5).
Short alternative routes are available near cities and along the coast.
Longer detours also characterise road sections along the Swedish border,
although alternatives become available there when the Swedish road network is
used. The link-failure likelihood varies between 0 and 0.02 events/year and
is highest in the north of Vestlandet (Fig. 6a), largely mimicking the
topographic susceptibility (Fig. 2a). Similarly, higher trigger frequencies
along the mountain plateaus contribute to an increase of this likelihood (Fig. 2b).
Estimated annual link risk expressed as vehicle km; main routes
between seven large cities in southern Norway are marked in yellow.
Illustration of network routing with (a) open access between Lom
and Skjolden and (b) under temporary closure of road between the two
cities. Legend to overview map is given in Fig. 7.
The total additional traffic load per road closure varies widely between
101 and > 106 vehicle km per day (Fig. 6b). The
highest loads may occur not only in the mountainous interior of the study area where
road density is low and excess distances are high but also near cities and
along the coast with commensurately high traffic volumes (Fig. 2c). We
computed the maximum loads for a road section stretching from Trondheim
towards the Swedish border. In addition to a large traffic volume of
> 25 000 cars/day, the excess distances are quite large
(> 300 km) along this section.
A high annual debris-flow-related link risk of > 1000 vehicle km year-1
characterises Vestlandet (Fig. 7), an area that combines high
topographic susceptibility, hydro-meteorological trigger frequencies, and
long excess distances. High traffic volumes near Bergen and Ålesund
exacerbate this risk. Parts of main routes linking the larger cities are
also tagged with high risks: 56 out of the 100 links with the highest link
risks are located on the main routes.
Summing up the link-failure likelihoods along routes between major cities in
the study area, we obtain the total path-failure likelihood (Table 1). In
this regard, the main route between Ålesund and Stavanger has the
highest likelihood of being blocked by debris flows with an average return
period of ∼ 10 years. A comparable blockage potential
characterises the routes Trondheim–Bergen, and Trondheim–Stavanger.
Similarly, all routes crossing the mountainous interior in north–south or
west–east direction have higher path-failure likelihoods than routes
circumventing this area.
Scenarios
Two scenarios highlight the applicability of our approach. In Scenario 1, we
identified a 75 km long road section on Riksveg 55 between Lom and Skjolden
as the section with the highest link-failure likelihood, which we expect
occurs every ∼ 50 years on average. Riksveg 55 is one of the
main interregional connections between Bergen and Trondheim used by
∼ 4000 cars/day. The scenario involves a road closure between
Lom and Skjolden (Fig. 8). The shortest detour between these villages is via
Stryn and has an excess distance of 240 km, i.e. more than 3 times
the original road section (Fig. 8b). The total additional traffic load would
be 960 000 vehicle km, assuming 1 day of road closure. Given a fuel
consumption of 6 L/100 km and a fuel price of EUR 1.5/L, this
total additional traffic load would incur top-on fuel costs of EUR 86 000.
With a return period of ∼ 50 years, the expected
annual detour costs are EUR 1720 for this road section only on the
premise that motorists take the calculated detour route irrespective of
their origin and destination (blue route, Fig. 8b). However, the shortest
detour between Bergen and Trondheim would not pass either Lom or Skjolden.
The alternative quickest route has an excess distance of 67 km, incurring
additional fuel costs of ∼ EUR 20 000, assuming a
daily traffic volume of 4000 cars between Bergen and Trondheim (yellow
route, Fig. 8b).
In Scenario 2, western Norway (Vestlandet) was hit by
extreme rainfall brought by low “Kristin”; local rainfall on 14 September 2005 exceeded
100–200 mm day-1 (Sletten, 2009). The area around Bergen experienced
particularly heavy rainfall that triggered a large number of debris flows.
At least 49 of these caused documented traffic disruption on several roads
and railways. In Bergen, 3 people died, 7 were injured, and 152
were evacuated (Bargel et al., 2011). Traffic on the main routes between
Bergen and cities in the east (Trondheim, Lillehammer, Oslo) were impacted
by debris flows, while routes in the west (Ålesund, Stavanger,
Kristiansand) remained accessible (Fig. 9a). Excess distances related to
these link failures vary considerably between the affected city connections
(Table 2); while the detour from Bergen to Oslo is just 13 km or 3 %
longer than the original route, the excess distance for the
Bergen–Lillehammer connection is 89 km or 21 % of original length.
On 15 November 2005, another extreme precipitation event (“Loke”) hit the
Norwegian west coast (Aall, 2013). Some 63 documented debris flows occurred
over a large area in the northern part of Vestlandet, causing massive rail
and road traffic delays. Again, main routes between Bergen and eastern cities
were disturbed (Fig. 9b), this time also including the main route to
Ålesund (Table 2). The computed excess distances from Bergen were
between 13 and 67 km to Oslo and Trondheim, i.e. 3 and 11 % larger
than the original distances respectively (Table 2).
Discussion
We quantified the failure likelihood of road links potentially impacted by
debris flows in southern Norway by merging estimates of topographic
susceptibility and hydro-meteorological trigger frequency. The national
mass-movement inventory (http://www.skrednett.no/; Jaedicke et al., 2009)
gives some insight into past road closures by debris flows: data from 2003
to 2007 demonstrate that the road links most frequently impacted by debris
flows have a substantially higher failure rate than our computed minimum
return period of ∼ 50 years suggests. The 4 years of
detailed data coverage, however, fall short of offering substantial
validation of our model concerning the simulated failure likelihoods. These
underestimates may partly result from a general improvement of the reporting
quality from 2003 to 2007 as opposed to the preceding years used for model
training. Nevertheless, the computed link-failure likelihoods are an
unprecedented attempt to rank at the regional scale the road-network
segments according to their propensity of disruption. This information is
vital concerning potential debris-flow impacts and is extensible to other,
more frequent, processes such as snow avalanches and rockfalls that share
similar topographic and climatic prerequisites (Slaymaker, 2010). Clearly
both appraisals of the susceptibility and triggers of snow avalanches and
rockfall would need due adjustment if added to our network analysis.
However, the results of our analysis present a first step towards a more
comprehensive risk assessment that includes the risk related to functional
damages exemplified by one specific type of rapid mass movement.
We quantified the failure likelihood for the shortest paths between major
cities in southern Norway, namely Oslo, Lillehammer, Trondheim, Ålesund,
Bergen, Stavanger, and Kristiansand. However, we did not account for
temporary closure during winter months, which is common for parts of these
connections. Hence, the seasonal occurrence probability of debris flows may
modulate our assessment of link- and path-failure likelihoods. Given that
most documented debris flows occurred in autumn, whereas winter months
are less affected by debris flows and related road closures, we surmise that
our annual likelihoods are minimum estimates. The available data on daily
traffic volume are averages, however, and thus do not allow resolving any
temporal pattern.
Distances between Bergen and other cities with intact road
network and excess distances following road closures specified in scenarios
1 and 2, given in km. Ratio of excess distance to original route length
shown in parentheses.
Scenarios investigating effects of extreme rainfall events
(a) “Kristin” and (b) “Loke” in 2005 and related debris flows along routes
between Bergen and other large cities in southern Norway.
Our computed excess distances relate necessary detours around a failed road
link to the original distances and draw on graph theory, which is a common,
straightforward, and mathematically rigorous method used in network analysis
(Holmgren, 2006; Grubesic et al., 2008). This approach requires a
well-documented road network without any topological errors (Erath et al.,
2009). International road connections may compromise this analysis: along
the Swedish border the computed excess distances are biased because we miss
possible shorter detours that make use of the Swedish road network.
Including the road networks beyond national borders is likely to yield more
robust results for some of the excess distances.
Our method of computing excess distances relies on topology but may neglect
a number of alternative options of dealing with closed roads. Two cases
require that the entire distance of the alternative route connecting both
ends of the link needs to be passed without much alternative: (1) regional
travellers have the two end vertices of the failed link as origin and
destination, or (2) interregional travellers are not aware of the road
closure until they reach the disrupted link in question. However, motorists'
knowledge about specific traffic conditions regarding potential detours is
another point that may compromise the validity of computed excess distances
(Lyons, 2006; Nyblom, 2014): drivers may be informed about road closures
well in advance and choose alternative routes that deviate from the
vertices enclosing the impassable road. This information status depends,
among others, on the time between the announcement of road closure and the
onset of journey, the distribution and reception of information by
authorities, and the technical capability of drivers to receive this
information. Our scenario-based assessment of such alternative paths between
larger cities in southern Norway demonstrates that prior knowledge concerning
road closures leads to significantly reduced excess distance (Fig. 4).
Scenario 1 indicates that the ratios of excess distances to the original
travel distance are larger for regional than interregional traffic.
Scenario 2 also illustrates that multiple link failures may prolong the shortest path
between cities in few cases only, e.g. in September 2005 between Bergen and
Lillehammer. These results hinge on the assumption that travellers are
informed about road closures and alternative paths do not suffer from
subsequent failures.
We stress that our network analysis focuses on the total additional traffic
load per road closure and not on any additional costs incurred by
structural road damage. Clearly, the total additional costs from detours
involve aspects of fuel consumption and availability, actual fuel pricing,
driving style, road type, local speed limits, and many others. We refrained
from including these parameters in our calculation because of their high
variability and favoured casting our risk estimates in vehicle distances per
year instead. Fuel consumption is not directly proportional to distance, and
actual numbers are subject to rapid price oscillations. However, if reliable
information is available, this parameter should be included in the risk
calculation to obtain monetary costs associated with detours. We also did
not account for the instance that car drivers would occasionally accept
small extra distances, e.g. the use of a road instead of a ferry, as waiting
times and travel speed will have a direct impact on the overall travel time.
Future road-network risk analyses may wish to devote more attention to such
effects of alternative transport modes, different road types, etc. on travel
time and fuel consumption.
Expressing the link-failure risk in annual vehicle kilometres is the major
contribution of our region-wide assessment of the functional value of
individual road network segments. This approach goes beyond standard
appraisals of road management strategies based on structural values alone.
This is because official stakeholders such as road and railway
administrations are usually more interested in the structural damage they
are paying for (Norem and Sandersen, 2012). Our computed potential costs
arising from detours due to debris-flow-related road closures are not
included in this bill and are shared amongst individual motorists. However,
these external costs are likely to increase if including transport of goods,
especially perishables, and delays in delivery in the risk analysis
(Bråthen, 2001). While costs related to time delay and fuel may be
affordable for the individual, these costs may become critical for companies
whose major income depends on the transport industry or the supply of goods
(Lakshmanan, 2010).
Conclusions
We coupled graph theory with quantitative risk assessment to estimate the
annual expected costs of detours arising from road closure by debris flows
in southern Norway. A combination of topographic susceptibility and
hydro-meteorological trigger frequency in first-order catchments formed the
basis for assessing the likelihood of a given road link to fail following
debris-flow impact. From this we estimated link-failure likelihoods that,
together with data on traffic volumes and computed excess distances,
resulted in risk estimates concerning the functional values of road links.
We expressed this risk as the expected additional total of annual vehicle
kilometres required for detours around closed road sections. Our study
concentrated on link-based calculations but also addressed scenarios of
path-failure likelihoods between larger cities and effects of debris flows
causing multiple road closures.
Debris-flow-related link-failure risk is highest in the mountainous interior
of southern Norway, a region that needs to be traversed in order to connect
the major cities. This high risk results from high link-failure likelihoods,
moderate traffic volumes, and high excess distances. Nevertheless, detour
options are manifold for these major trunk routes with only little
additional costs provided that drivers are sufficiently well informed about
road closures. Our analysis indicates that effective reduction of these
costs requires timely publication of information pertinent to road closure.
Overall, we estimate this risk at ∼ 10–1000 additional vehicle
kilometres per year. This estimate may be readily converted to monetary
costs where data on fuel cost and consumption are available. We stress that
these anticipated costs, although likely to be shared by individual
motorists, are minimum costs. Companies relying on timely delivery of goods
and perishables may wish to consider these and additional costs that arise
from undue delays because of debris-flow-related
road closure in their
risk portfolio.
Acknowledgements
Wolfgang Schwanghart and Oliver Korup acknowledge financial support by the
Potsdam Research Cluster for Georisk Analysis, Environmental Change, and
Sustainability (PROGRESS). Farrokh Nadim and Nele Kristin Meyer thank the
InfraRisk research project and the International
Centre for Geohazards (ICG) for the
financial support. We thank David Gleich (Purdue University) for
providing access to MatlabBGL.
Edited by: F. Guzzetti
Reviewed by: two anonymous referees
ReferencesAall, C.: Tilpassing til klimaendringar – frå justeringssamfunnet til
transformasjonssamfunnet. Working seminar ”Rullering av klimaplan for
Hordaland – temagruppe klimatilpassning”, Bergen, Presentation, available
at http://www.hordaland.no/PageFiles/53480/KlimaCarloAallN.pdf (last access: 21 February 2014),
2013.
Andrey, J.: Long-term trends in weather-related crash risks, J.
Trans. Geogr., 18, 247–258, 2010.
Appert, M. and Chapelon, L.: Measuring urban road network vulnerability using
graph theory: the case of Montpellier's road network, HALSHS working paper,
2013.
Bargel, T. H., Fergus, Å. T., Devoli, G., Orvedal, K., Peereboom, I.,
Øydvin, E. K., Stalsberg, K., Slatten, K., Fischer, L., Rubensdotter, L.,
and Eilertsen, R.: Plan for skredfarekartlegging – Delrapport jordskred og
flomskred, NVE report, Oslo, 16, 2011.
Berdica, K.: An introduction to road vulnerability: what has been done, is
done and should be done, Trans. Pol., 9, 117–127, 2002.
Bjordal, H. And Helle, T. E.: Skred og flom på veg., SVV report, Oslo, 5, 2011.
Boge, K.: Votes count but the number of seats decides, Doctoral
dissertation, Norwegian School of Management Oslo, 2006.
Bråthen, S.: Do fixed links affect local industry? A Norwegian case
study, J. Trans. Geogr., 9, 25–38, 2001.
Demšar, U., Špatenková, O., and Virrantaus, K.: Identifying
critical locations in a spatial network with graph theory, Trans.
GIS, 12, 61–82, 2008.
Dilley, M.: Natural disaster hotspots: a global risk analysis, World Bank
Publications, Washington D.C., 5, 2005.
Downing, T. E., Butterfield, R., Cohen, S., Huq, S., Moss, R., Rahman, A., Sokona, Y.,
and Stephen, L.: Vulnerability indices: climate change impacts and adaptation, UNEP
Policy Series, UNEP, Nairobi, 2001.
Dyrrdal, A. V., Isaksen, K., Hygen, H. O., and Meyer, N. K.: Changes in
meteorological variables that can trigger natural hazards in Norway, Clim.
Res., 55, 153–165, 2012.
Erath, A., Löchl, M., and Axhausen, K. W.: Graph-theoretical analysis of
the Swiss road and railway networks over time, Net. Spat.
Econom., 9, 379–400, 2009.
Fischer, L., Rubensdotter, L., Sletten, K., Stalsberg, K., Melchiorre, C.,
Horton, P., and Jaboyedoff, M.: Debris flow modeling for susceptibility
mapping at regional to national scale in Norway, in: Proceedings of the 11th
International and 2nd North American Symposium on Landslides, Banff, Canada, 06/2012, 3–8, 2012.
Gross, J. L. and Yellen, J.: Graph theory and its applications, CRC press,
Boca Raton, Florida, 2005.
Grubesic, T. H., Matisziw, T. C., Murray, A. T., and Snediker, D.: Comparative
approaches for assessing network vulnerability, Int. Reg.
Sci. Rev., 31, 88–112, 2008.
Heckmann, T., Schwanghart, W., and Phillips, J. D.: Graph theory – recent
developments of its application in geomorphology, Geomorphology, in press, 2015.
Holmgren, Å.: Using Graph Model to Analyze the Vulnerability of Electric
Power Networks, Risk Anal., 26, 956–969, 2006.
Immers, B., Stada, J., Yperman, I., and Bleukx, A.: Towards robust road
network structures, Slovak J. Civil Eng., 12, 10–17, 2004.Jaedicke, C., Lied, K., and Kronholm, K.: Integrated database for rapid mass
movements in Norway, Nat. Hazards Earth Syst. Sci., 9, 469–479,
10.5194/nhess-9-469-2009, 2009.
Jenelius, E.: Network structure and travel patterns: explaining the
geographical disparities of road network vulnerability, J. Trans.
Geogr., 17, 234–244, 2009.
Jenelius, E.: Large-scale road network vulnerability analysis, Doctoral
dissertation, KTH Stockholm, 2010.
Lakshmanan, T. R.: The broader economic consequences of transport
infrastructure investments, J. Trans. Geogr., 19, 1–12,
2010.
Lyons, G.: The role of information in decision-making with regard to travel,
IEEE Proc. – Intelligent Transport Systems, 153, 199–212, 2006.Meyer, N. K., Dyrrdal, A. V., Frauenfelder, R., Etzelmüller, B., and Nadim,
F.: Hydrometeorological threshold conditions for debris flow initiation in
Norway, Nat. Hazards Earth Syst. Sci., 12, 3059–3073,
10.5194/nhess-12-3059-2012, 2012.
Meyer, N. K., Schwanghart, W., Korup, O., Romstad, B., and Etzelmüller,
B.: Estimating the topographic predictability of debris flows,
Geomorphology, 207, 114–125, 2014.
Murray, A. T. and Grubesic, T. H.: Critical Infrastructure, Springer Berlin
Heidelberg, 2007.
Norem, H. and Sandersen, F.: Flom- og sørpeskred. Project report ”Klima
og Transport”, SVV report, Oslo, 73, 2012.
Nyblom, Å.: Making plans or just thinking about the trip?
Understanding people's travel planning in practice, J. Trans.
Geogr., 35, 30–39, 2014.
Schulz, C.: Identification of critical transport infrastructures, Forum
DKKV/CEDIM: disaster reduction in climate change, Karlsruhe, 15, No. 16.10, 2007.Scott, D. M., Novak, D. C., Aultman-Hall, L., and Guo, F.: Network
robustness index: A new method for identifying critical links and evaluating
the performance of transportation networks, J. Trans. Geogr.,
14, 215–227, 2006.
Siek, J. G., Lee, L. Q., and Lumsdaine, A.: The Boost Graph Library: User
Guide and Reference Manual, Pearson Education, Upper Saddle River NJ, 2001.
Slaymaker, O.: Mountain hazards, in: Geomorphological Hazards and Disaster Prevention,
edited by: Alcántara-Ayala, I. and Goudie, A., 33–48, 2010.Sletten, K.: GeoExtreme prosjektet. Project seminar “GeoExtreme –
endringer i klima og skredfare de neste 50 år”, Oslo, Presentation,
available at: http://www.geoextreme.no/seminar.htm (last access: 21 February 2014), 2009.
Tacnet, J. M., Mermet, E., and Maneerat, S.: Analysis of importance of road
networks exposed to natural hazards, Proceedings of the AGILE'2012
International Conference on GIS, Avignon, 24–27 April 2012, 370–375, 2012.
Taylor, M. A. and D'Este, G. M.: Concepts of network vulnerability and
applications to the identification of critical elements of transport
infrastructure, New Zealand Transport Research Forum, 1–15, 2003.
Taylor, M. A., Sekhar, S. V., and D'Este, G. M.: Application of
accessibility based methods for vulnerability analysis of strategic road
networks, Netw. Spat. Econom., 6, 267–291, 2006.
The MathWorks.: MATLAB, ver 2012a, The MathWorks Inc., Natick, MA, USA, 2012.
Winter, M. G., Macgregor, F., and Shackman, L.: Scottish road network
landslides study: Implementation. Summary report, Transport Scotland, 2008.