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Evaluating road network damage caused by natural disasters in the Czech Republic between 1997 and 2010
Transportation Research Part A 80 (2015) 90–103
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Transportation Research Part A journal homepage: www.elsevier.com/locate/tra
Evaluating road network damage caused by natural disasters in the Czech Republic between 1997 and 2010 Michal Bíl ⇑, Rostislav Vodák, Jan Kubecˇek, Martina Bílová, Jirˇí Sedoník CDV Transport Research Centre, Líšenˇská 33a, Brno 636 00, Czech Republic
a r t i c l e
i n f o
Article history: Received 20 October 2014 Received in revised form 8 July 2015 Accepted 14 July 2015 Available online 15 August 2015 Keywords: Road network Network efficiency index Network damage Natural disasters Vulnerability Czech Republic
a b s t r a c t Road networks play a vital role in maintaining a functioning modern society. Many events perceptibly affect the transport supply along these networks, especially natural disasters such as floods, landslides, and earthquakes. Contrary to more common disruptions of traffic from accidents, or maintenance closures, natural disasters are capable of destroying large numbers of roads and usually cover vast areas. When evaluating network damage no single measure alone is able to describe the full extent of network destruction. In this study, we investigated six highly damaging natural disasters, which occurred in the Czech Republic between 1997 and 2010. They were all induced by extreme rainfall or by rapid snowmelt and resulted in floods and landslides. Their impacts are evaluated with respect to the damage to road networks and decreased serviceability. For mutual comparison of the impacts and their analysis we used several criteria, described in the paper, related to economic impacts, physical harm to individuals and infrastructures, and the effects on connectivity and serviceability. We also introduced a new measure based on the network efficiency index which takes into account the importance of nodes based on their population. Moreover, we provide a detailed analysis of one such event in July 1997 that significantly affected the road network of the Zlín region. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Damage to road networks by natural disasters Natural disasters (e.g. floods, landslides or earthquakes) are frequent causes of road network damage. Compared with other common traffic disruptions, such as traffic accidents and maintenance closures, these natural events may completely destroy transport infrastructure in a given area and cause the long-term cut-off of inhabitants from the main network (Eleutério et al., 2013), as well as appreciable economic losses (e.g. Anbazhagan et al., 2012). Well-known events which have seriously impacted road networks include the Loma Prieta earthquake which hit the San Francisco Bay area in 1989, the 1994 Northridge earthquake in the Los Angeles metropolitan area, and the 1995 disaster in the Kobe region (Chang and Nojima, 2001). The common feature was serious damage to the road network, specifically the highways. A comprehensive overview of road damages due to earthquakes and their classification is presented by Anbazhagan et al. (2012). Besides such exceptional disasters there are others which are caused primarily by heavy rains (and subsequent floods or landslides).
⇑ Corresponding author. Tel.: +420 548 641 795; fax: +420 548 423 712. E-mail address: [email protected] (M. Bíl). http://dx.doi.org/10.1016/j.tra.2015.07.006 0965-8564/Ó 2015 Elsevier Ltd. All rights reserved.
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These produce rather minor overall damage but may also disrupt the road network within a large region (e.g. Vinet, 2008; Hilker et al., 2009). 1.2. Road networks and their resistance to incidents Road networks can be depicted as a specific kind of communication network represented by graphs. This allows one to study the consequences of various events on their. The events can be caused consciously as a form of intentional attack or unconsciously as natural disasters (see Albert et al., 2000; Dall’Asta et al., 2006). In the second case the events contains certain form of randomness. In this work we pay attention to the second type of events. The most studied problems cover the concepts of vulnerability and robustness of a road network infrastructure (e.g. Murray and Grubesic, 2007; Matisziw et al., 2009; Reggiani, 2013). The term ‘robustness’, from the view of the whole road network and its ability to ensure the accessibility of an area, refers to its capability to absorb a certain amount of disrupted links (Berdica, 2002). A robust network should include a certain amount of link redundancy, so that a small disruption would not lead to collapse, defined as a system-wide decline into several disconnected parts. However, there are some limitations on why real road networks cannot have maximal robustness. The problem is that the more robust the network, the more redundant it is. It means that such a network will be more expensive and demanding of maintenance. Moreover, road networks are significantly influenced by the relief topography, which may sometimes become a dominant factor in determining their structure (Rodrigue et al., 2010). At the opposite extreme, the most vulnerable or ‘least robust’ (see Berdica, 2002) network will disintegrate into two parts (in graph theory called components, e.g. Newman, 2010) after any link is taken away. Mountain valleys are often weakly connected with the rest of a network and the disruption of one or two links often leads to a complete cut-off of nearby inhabitants. Thus, the aim of a vulnerability analysis is to identify those critical links in a network (e.g. Bell, 1999; Berdica, 2002; Jenelius et al., 2006; Sohn, 2006). It is important to say that network vulnerability is not dependent on probability; it represents the consequences of an event (see Berdica, 2002). It follows from the definitions of robustness and vulnerability of road networks that both concepts are fundamental for the analysis of consequences of natural events. Two features of natural disasters are important to note. First, such natural events are characterized by some randomness in their occurrence. Second, the events can affect the most vulnerable links in the network and thus maximize their impact. Moreover, new weak links may emerge as a result of partial network damage which are necessary for the proper performance of the rest of the network. 1.3. Measuring the network damage To obtain any information about the robustness and vulnerability of road networks and about the impact of natural events it is necessary to establish some suitable measures. When measuring the impact of a disaster, overall economic losses are generally used for comparison. A loss of connection and reduced accessibility is often a result of such catastrophes, however. Comparison of pre- and post-disaster network performance is therefore possible using suitable indices connected with robustness. There are numerous studies which estimate and measure impacts of various natural disasters on infrastructure, including roads. When evaluating damage caused by a disaster, direct losses are usually computed (e.g. overall damage to infrastructure). From the view of network performance the indirect losses may be also important (Yee et al., 1996). Versini et al. (2010) evaluated the vulnerability of roads in connection with flooding on the basis of geographic information and actual flooded road segments over the last 40 years in the area around Gard, France. The impact of the earthquake in Haiti on the accessibility of humanitarian aid was summarized by Bono and Gutiérrez (2011). They applied GIS spatial analysis to show changes in accessibility for the affected towns. Chang and Nojima (2001) evaluated the traffic system performance for the city of Kobe, which was affected by an earthquake in 1995 and compared it with antecedent earthquake events in the USA (Loma Prieta in 1989 and Northridge in 1994). Their study used a ratio of the lengths of damaged and undamaged road networks. They also used an accessibility ratio which is based on distance in computation of the length of a path between two nodes. When the network is broken up into two and more components, however, their measure stretches to infinity, because it is impossible to find finite paths among nodes from these components, and the ratio is therefore unusable. Another shortcoming of previously published methods is that they compute changes from one simultaneously closed network link (e.g. Jenelius et al., 2006). This could be still used when modeling the effect of traffic accidents or the planned closure of a link. However, natural disasters are capable of damaging many roads at one time. This means the information we have about the current state of a network and flows in it (see for instance Louail et al., 2015; Gallotti and Barthelemy, 2015; Lenormand et al., 2014a,b) are dramatically changed. The common traffic pattern (Gottlich and Klar, 2009; Lammer et al., 2006; Helbing, 2002, 2001) completely disappears and the standard traffic control begins to be useless. The state of the transportation system also differs significantly from common traffic congestions (Treiber et al., 2000) and therefore is not in equilibrium (Kurauchi et al., 2009). This is the reason why there is a need to take a different view of the network after certain events which result in the disintegration of the network. Thus it is also necessary to analyze the resilience of the network (see Cimellaro et al., 2010; Arcidiacono et al., 2012).
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However, some of the methods, which were originally developed and used for analysis of the impact of several closed links, can be used or modified for natural disasters (e.g. Sohn, 2006). Other suitable methods for evaluation of damage to the entire network can be found in other fields, especially network science. Yin and Xu (2010) introduced a network efficiency index, which is capable of evaluating a disintegrated network; one that is breaking up into many separated parts or components. The index is based upon the indices developed in Latora and Marchiori (2004). Such a measure is therefore suitable when comparing pre- and post-disaster road network performance. One potential improvement to this index can be found in Dangalchev (2006), where the influence of longer detours is reinforced. The aim of this work is to demonstrate the impacts of natural disasters which affected the Czech Republic (CZ) between 1997 and 2010, from a perspective of the road network performance and overall damage. The work is organized as follows: Data, its collection and database preparation is presented in Section 2. The methods used for network damage evaluation are described in Section 3. Section 4 presents the results which are further discussed in Section 5.
2. Data 2.1. Natural disaster events Forms of road damage can be characterized by the following three levels: Total destruction, when the road embankment has to be reconstructed. Partial damage, when the road section is also closed, but the only subsequent work involves repairs to the road surface or minor stabilization of the road embankment. Closure due to temporal flooding or sedimentation (e.g. of mud from a field). This type of interruption does not require almost any repairing work. In this study we focused on the first two types of road closures, which require reconstruction and are usually long lasting. The road sections belonging to the third case may be opened to traffic in few hours and thus they are not important for our study. For this reason we also ruled out two disaster events connected with the transition of the deep low pressure storms known as Kyrill (January 2007) and Emma (March 2008), which resulted in many interrupted roads due to tree fall, but no significant road damage.
2.2. GIS data The Czech Road and Motorway Directorate provided a shapefile of the Czech road network. The data in this file is topological. The data on the number of inhabitants and the location of individual buildings were provided by the Czech Statistical Bureau. The shapefile of the road network which was used for the network analysis contains a simplified geometry where every link is a straight line and individual links are connected in nodes which are in the form of junctions. Nevertheless, the network topology is preserved. The attributes of the links include the real length of each segment. Analyses were performed for whole regions in order to assess the changes in accessibility among individual towns and villages. Therefore, the data do not include the street networks in towns and villages. Every town and village is represented by a node. In the case of larger towns, located on opposite sides of river banks, they may be represented by two or more nodes. Data were processed in GIS software ArcGIS 10.1 (for the preparation of road networks for other analyses), Scilab (for the computation of indices and components). Figures were created using CorelDRAW Graphics Suite X5.
2.3. Database on road section damage We produced a database of road sections damaged or closed due to natural events in the Czech Republic. Similar databases have also been compiled in other countries (e.g. Hilker et al., 2009; Papagiannaki et al., 2013). In the first phase we prepared and sent questionnaires to local road network administrators to indicate places and dates where disruption or damage to a road section occurred due to a natural disaster. This work started in 2011 and focused on the period between 1997 and 2010. As of May 2013, our database of affected road sections had 2752 records. By using exact dates of the interruptions for the road sections, we were able to delimit areas which were affected by the same event. Due to the fact that natural processes such as local floods or landslides occur quite frequently, we set a limit for concurrently interrupted road sections to define a network-wide important event. This limit (41 roads) is an average number of closed road sections (for any reason) in the whole CZ road network per day. It was derived from the on-line system of traffic information (www.dopravniinfo.cz). This number does not contain information on interrupted streets within built areas of cities and towns.
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2.4. An overview of the main natural disasters since 1997 The following storm and flood events were used in this study to assess impacts on transportation networks.
2.4.1. July 1997 This event occurred as a result of five days of precipitation (July 4–8) which reached 433 mm and exceeded the monthly average for July by nearly four times (Krejcˇí et al., 2002). The consequence was the most intense flood of the last 100 years, especially on the Morava River. Due to the geological conditions in the eastern part of the Czech Republic which is formed by landslide-susceptible flysch rocks, hundreds of landslides occurred. Many of them damaged residential houses, roads and railways.
2.4.2. August 2002 Within the 6–8th and again the 9–13th of August 2002, two deep cyclones passed through Central Europe (Ulbrich et al., 2003). An area of the Czech Republic was struck by the tail of these storms. Both moved slowly and therefore the rainfalls were long-lasting. Notably the second cyclone whose center moved directly over the western part of the Czech Republic caused extreme precipitations (Hladny´ et al., 2005; Kaspar and Müller, 2008). Between the 6 and 15th of the August up to 450 mm of precipitation fell.
2.4.3. April 2006 The winter of 2005/2006 was exceptional in terms of a very thick snow cover. This snow stayed until the end of March when higher air temperatures and heavy rainfall appeared, due to changes in air mass circulation over Europe. The first significant rain fell on March 26, which was followed on March 28–29 by further rains. This period yielded up to 35 mm of rainfall. The consequence was major flooding throughout the Czech Republic and more than 100 landslides in Moravia (Bíl and Müller, 2008; Klimeš et al., 2009).
2.4.4. June 2009 For Central Europe it is typical for air masses to circulate generally from the west to the east. It is more unusual for moist and warm air to flow to the Czech Republic from the east, especially during the summer. These events are often connected with intense storms. This type of circulation occurred at the turn of June and July 2009. This event was special due to its exceptionally long duration of almost two weeks (22th June–4th July), whereas a normal duration is 3–4 days. It was the longest period with this type of circulation for the last 63 years. In two meteorological stations precipitation exceeded 120 mm/2 days, in four others it exceeded 60 mm/h and in two others it exceeded 30 mm/15 min (MZP, 2009). The discontinuous area affected by this event (see Fig. 3) resulted in multiple isolated storms which caused extensive damage.
2.4.5. May 2010 Extreme precipitation occurred in the second part of May and at the beginning of June 2010 in the broader area of Central Europe. Watersheds were already saturated by an unusually wet May and were not able to accommodate another rainfall. The event can be divided into two phases between 15–20th of May and 30th May–3th June. At some stations rainfall topped 100 mm in 6–8 h. In the affected areas, three-day precipitation exceeded 80 mm, and some saw as much as 300 mm. Floods and landslides were also registered (Pánek et al., 2011).
2.4.6. August 2010 Two episodes with convectional rainfalls within 6–8th and 13–15th of August 2010 caused extreme floods in the north-western part of the Czech Republic. Maximal daily precipitation was about 180 mm, while the three days total (between 6 and 8th) reached 300 mm (Kubát et al., 2010).
3. Methods We used several metrics for analyzing a network undergoing some kind of disruption.
3.1. The number of broken or damaged road links The overall number of damaged road links is usually well known and may be used in absolute and relative numbers to all the road links. It is therefore possible to state the relative impact of an event and compare it to events on other networks with different size.
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3.2. The ratio of network lengths This index was used by Chang and Nojima (2001) and compares lengths of a network before and after a disaster. If a road link is broken, it is no longer available for transport and therefore its entire length, regardless the extent of the actual damage, is not taken into computation. 3.3. Network components In the case of exceptionally damaging natural disasters, a large number of links may be disrupted and the network would disintegrate into several components. The number of components and their size also show the impact of natural disasters (Fig. 1). 3.4. The number of people cut off from the main road network If we know the number of inhabitants for each node, we may also find out how many people likely remained cut off from the main network in individual components. From a practical point of view the main concern should be the number of people that remained cut off. We express both the absolute number of people affected by road disruption and a ratio to overall population within the respective region. 3.5. Network efficiency index To evaluate the disruption of a damaged network, we use an approach based upon the closeness centrality (e.g. Newman, 2010). This approach compares the disrupted network’s average efficiency (index Et) with the average efficiency of an undamaged network (index E) and provides us information about the network efficiency Vt given by the relation (see Yin and Xu, 2010)
Vt ¼
E Et E
where
E¼
X1 1 NðN 1Þ i–j dij
ð1Þ
1
and Et ¼
2
nodes s
X 1 1 NðN 1Þ i–j dij
1
ð2Þ
2
nodes s
where N is number of nodes and dij and dij represent the shortest path (in terms of number of links) between a node pair (i, j) in the undamaged and damaged network, respectively. Relation (1) is in fact a modification of the importance of a node from Latora and Marchiori (2004). The corresponding value of Vt is within the interval [0, 1] and measures a drop in network performance (or network serviceability, see Berdica, 2002) if some type of disruption occurs (Fig. 2). The importance of the Vt consists in its ability to describe the performance of the entire network, including separated parts (components). 3.6. Weighed network efficiency index Index Vt has one disadvantage. It cannot depict the importance of the individual nodes. This importance can be measured by the people living in the nodes (see Taylor et al., 2006). Thus we suggest a modification of (1) which looks as follows:
V tp ¼
Ep Etp Ep
ð3Þ
where
Ep ¼
X Pi Pj 1 NðN 1Þ i–j dij
"
2
people
2
nodes s
# and Etp ¼
X Pi Pj 1 NðN 1Þ i–j dij
"
2
people
2
#
nodes s
ð4Þ
Fig. 1. Examples of possible impacts of two simultaneously disrupted links (L). In the first case (A) one cut-off component (C) with six nodes (N) will emerge, in the second case (B) two cut-off components, each with only one node emerges.
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Fig. 2. An example of Vt computed for two types of interruption on a hypothetical network. In the first case (A) Vt = 0.056338, in the second (B) Vt = 0.2647887. This number is also possible to read as degree by which the serviceability of the network was reduced (by 5.6% or by 26% respectively).
Pi represents the number of people living in node i. In fact, it can be said that the importance of the shortest path between nodes i and j is directly proportional to the number of people living in nodes i and j and inversely proportional to the length of this path. This modification of the index can also be understood as a simple incorporation of a travel demand into our calculation. This enables us to measure the efficiency of the network under the assumption that the travel demand is not changed after the event. This is not always a realistic assumption because it is impossible to estimate a change in travel demand after such an event. However, we use both indices to analyze the impact of the event. We assume that they measure extreme cases which may appear, i.e. the case when the travel demand remains unchanged and the case when there is no travel demand and all nodes have the same importance. We refer the reader to Crucitti et al. (2006) for modification of (1) in case of geographical analysis. The methods used differ in computational-time demand. While the simplest method which evaluates the absolute numbers of broken links or their ratios into unbroken links is easy to derive within a GIS, the network-based methods including Vt and Vtp required from tens of minutes up to several hours. A topological structure of the networks had also been kept to allow for the shortest path algorithms. 4. Results 4.1. Extent and economic impact of the natural disasters On the basis of the data on road disruptions (see Section 2.3) we generated a map with the extents of the six natural disasters (see Section 2.4) which affected the road network of the Czech Republic between 1997 and 2010 (Fig. 3). The real extent of the areas with extreme precipitation may slightly differ, but for the delimitation of the events the recorded disruption of road links was substantial. In 1997, the most affected areas were in the eastern part of the Czech Republic, whereas in 2002 it was the western part. The event in 2006 had the largest spatial extent. The 2009 event had a discontinuous area of road disruption. In 2010, the first event struck the eastern part of the Czech Republic while the second event struck the northeastern part. We adjusted the published economic losses in relation to known inflation and to planned expenses of the state budget. Without these corrections we could get erroneous results which would overestimate impacts of the newest events (e.g. Barredo, 2009). In human and economic costs, the most devastating event was the 1997 event (see Table 1); 60 people died and after taking inflation into account, direct costs exceeded 100 billion (109) CZK. This was about 11% of the planned income of the state budget in the same year (Table 1). The 1997 event was also the first large flood which struck the Czech lands after a long period with little flooding. The last recorded floods of the same extent in the area were recorded at the turn of 19th and 20th centuries (Brázdil and Kirchner, 2007). The 1997 event was therefore exceptional in size and magnitude and nearly unprecedented. As such, there were no functional and tested crisis plans and warning systems. Another large flood hit the western part of the Czech Republic in August 2002. The losses were significantly lower despite the fact that the affected area was larger (49% vs. 41%) and that Prague, the Capital, was flooded as well. Also, fatalities were one third of those that occurred in 1997. The gradual progress of floods in 2006 and better readiness contributed to the fact that the losses from these were lower, though still 7 billion CZK. The series of isolated flash floods in 2009 hit 36% of the Czech Republic and resulted in 9 billion CZK loses. In May 2010, the floods, which were not extensive (only 13.5% of the Czech Republic) caused a relatively large amount of damage (5 billion CZK). It was the third event when landslides occurred in significant numbers and damaged roads. In August 2010, an area in the northern part of the Czech Republic was hit by devastating floods. Losses computed to area units were comparable to those in 1997. It hit only 4% of the Czech Republic, but the overall losses were 10 billion CZK. 4.2. Impact evaluation of the road networks from the view of regional administrative units Due to the fact that the roads (excluding highways and first class roads) are managed by local administration units (regions) and due to the extreme computation demands for determining indexes Vt and Vtp we evaluate the impacts of natural disasters in regional networks. To keep the network intact and prevent what might appear to be artificial dead-end links,
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Fig. 3. Delimitation of the six most important natural disasters was made on the basis of recorded damage to roads.
Table 1 Extent and impacts of natural disasters since 1997. Year, month
Extent (km2/% area CZ)
Overall losses in 109 CZK
Losses per unit area (109 CZK/km2)
Ratio of losses to planned income of the state budget (%)
Losses to transport infrastructure (109 CZK)
Disrupted road links
Fatalities
1997, 2002, 2006, 2009, 2010, 2010,
32,607/41.3 38,442/48.7 47,644/60.4 28,324/35.9 10,698/13.5 3312/4.2
102.4 89.4 6.9 8.7 5.2 10.1
3.14 2.33 0.14 0.31 0.49 3.05
11.40 10.60 0.68 0.76 0.50 0.98
19.6 11.6 2.5 3.9 1.9 3.2
300 174 137 141 108 129
60 19 9 15 3 5
7 8 4 6 5 8
All losses were computed in Czech crowns (26 CZK 1 €) and inflation was taken into account according to data provided by the Czech National Bank (www.cnb.cz).
we kept the existing detour routes beyond the borders of the regions. The results, ordered according to index Vt, are shown in Table 2. The worst of the affected areas in almost all parameters was the Zlín region (ZLK) in July 1997. Index Vt shows that ZLK road network serviceability was reduced by almost 30% in July of 1997. When taking into account the number of people in the nodes the Vtp was almost 33%. The ratio of networks lengths (L) drop to 78.4%. The second and the third most damaged regions according to Vt were Moravskoslezsky´ region (MSK) and Olomoucky´ region (OLK), both also in July 1997. The serviceability of their networks was lowered by about 10%. The other parameters between the two regions differed significantly: MSK 1997 was hit in places where relatively few people lived (1.3%) in contrast to OLK (6.1%). This is also supported by the Vtp values. The network of MSK was disintegrated into 32 components which resulted in 40 cut off nodes, whereas OLK fell apart into only 14 components but with 107 nodes off the main network. The results for OLK 1997 are also interesting because a relatively few disrupted road links (2.7%) caused the cut off of quite a large number of nodes (7.4%). In the rest of the regions and events this ratio was usually reversed. For the entire set of regions (in Table 2) a drop in serviceability by more than 5% was recorded in only 7 cases. In the rest of the 19 cases the Vt was between 0.004 and 0.037 (0.4–3.7% decrease). When considering people in nodes, Vtp, the situation remains quite similar to Vt with two exceptions: Jihocˇesky´ region (JHC) 2002 and MSK 1997 (Fig. 4). In JHC 2002 only 0.3% people were cut-off, but paths among the inhabited nodes were
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M. Bíl et al. / Transportation Research Part A 80 (2015) 90–103 Table 2 Impacts of natural disasters on regional road networks. Region
ZLK MSK OLK ZLK LBK JHC ULK JMK LBK MSK ULK ZLK JHC OLK PAK KVK JMK PAK ZLK OLK JHC STC ULK OLK MSK JMK a
Year
1997 1997 1997 2010 2010 2002 2010 2006 2009 2010 2002 2006 2006 2009 2006 2002 2009 1997 2009 2006 2009 2002 2009 2010 2009 2010
Month
7 7 7 5 8 8 8 4 7 5 8 4 4 6 4 8 7 7 6 4 7 8 7 5 7 5
Vt
0.30 0.10 0.10 0.09 0.09 0.08 0.07 0.04 0.04 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00
Vtp
0.33 0.05 0.08 0.09 0.06 0.18 0.06 0.02 0.04 0.01 0.03 0.03 0.01 0.01 0.02 0.01 0.01 0.02 0.02 0.02 0.00 0.01 0.01 0.00 0.00 0.00
Damaged links Abs.
%
121 98 52 28 39 91 68 24 21 39 34 14 38 20 37 10 34 20 5 13 15 30 14 9 10 13
13.1 6.4 2.7 3.0 3.2 3.2 3.0 1.1 1.7 2.6 1.5 1.5 1.3 1.0 1.9 1.1 1.5 1.0 0.5 0.7 0.5 0.5 0.6 0.5 0.7 0.6
La
78.4 88.9 95.2 95.3 94.8 95.2 94.5 97.9 97.6 94.2 97.3 97.7 97.5 97.6 96.7 97.5 97.8 98.0 99.7 98.7 99.3 99.2 98.6 99.0 98.6 98.8
Components
47 32 14 11 12 18 19 4 4 7 11 5 7 8 4 4 5 5 2 4 3 4 3 1 2 1
Cut off population Abs.
%
67,442 17,418 44,245 16,932 11,112 1996 8042 2844 1126 2862 3491 2470 284 5665 452 935 843 876 280 2479 38 610 340 0 228 0
11.3 1.3 6.1 2.8 2.6 0.3 0.9 0.2 0.3 0.2 0.4 0.4 0.0 0.8 0.1 0.3 0.1 0.2 0.1 0.3 0.0 0.1 0.0 0.0 0.0 0.0
Ratio of broken and unaffected networks after Chang and Nojima (2001).
Fig. 4. The relation between Vt and Vtp. It is clear that Vt alone cannot give a true picture in a situation when inhabitants are distributed unevenly within a network or when damaged roads were important for traffic. The term importance means here that the road is a part of an optimal route between nodes.
seriously affected and therefore the index’s rise was based on the relative elongation of important paths among those heavily populated nodes (see Fig. 5). Whereas in JHC 2002 the road network was not impacted to a large extent, in MSK 1997 the road network (network topology) was damaged seriously. Roads connecting localities with few or no people were predominantly affected or blocked.
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Fig. 5. The road situation in JHC 2002, where only 0.3% of the people were cut-off and also Vt was only 7.9. Due to the fact, that the main roads lying on the shortest paths among the largely inhabited areas were affected (see the damaged roads in the central part of JHC around heavily populated nodes), the Vtp raised to 18.0.
4.3. Zlín region in July 1997 As was stated above (Table 2), the ZLK region in 1997 was the worst affected region of those we studied. In order to illustrate our method of analysis, we will depict the impacts of this event in detail. As a result of floods and landslides the road network of ZLK broke up into 46 separate components. At first it was difficult to connect the separated parts of the area. Urgent medical cases were secured by the air rescue service. Helicopters provided drinking water and food. The most damaged road segments were repaired only provisionally with procedures such as temporary bridging. In total 121 of the 923 links were disrupted (13.1%). Some of them were disrupted in more than one part, but the majority of them were disrupted in one locality. The total length of these disrupted links was 452 km. This is not the total length of the road in question, but the length of the links which were disrupted anywhere between two nodes. The main component was formed of 641 nodes out of the total number of 723 (which formed 89% of the intact network). The other components had substantially fewer nodes. The largest one of them (component No. 2, see Fig. 6) had 13 nodes and the others had between 1 and 7 nodes. There were 9 components with 2 nodes and 32 components had only one node (Fig. 7). Regarding the number of inhabitants, the situation was slightly different. The majority of the inhabitants were located within the main component. There were 528,211 inhabitants, which also constituted 89% of all 595,653 inhabitants of the Zlín region. The second largest number of inhabitants was located in component No. 15 (10,031 inhabitants), which was formed by a single node – a part of the town of Uherské Hradišteˇ near the Morava River (Fig. 7). At that time the town was divided into 3 parts and separated from the rest of the network. The second largest component with 13 nodes was located in the eastern part of the region and contained 6168 inhabitants (see Fig. 8, component No. 2). We also analyzed locations of the components relative to the main component. This is important when there is a need to reconnect the network. To access 38 out of 46 components from the main component just one link needed repair. The other 8 components, however, were located ‘behind’ other components. They were reachable through two (6 cases) or even three (2 cases) damaged links (see components No. 30 and 35, Fig. 8). This example occurred in the closed mountain valley in the spring area of the Vsetínská Becˇva River.
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Fig. 6. The situation in ZLK 1997.
Fig. 7. The road network of ZLK around the town of Uherské Hradišteˇ disintegrated in July 1997 into four components. The town itself was divided into three main parts. The largest one contained about 10,000 people.
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Fig. 8. ZLK 1997 – the eastern part of the region, where many components originated, and from which two (No. 30 and 35), were separated from the main network by 3 disrupted links.
It means that the term component may refer to a different degree of remoteness, determined not only by the pure distance from the main network in meters but also by a number of broken links which have to be repaired before the component can be reached. We can thus determine the minimal number of steps (in terms of repaired road sections), which are necessary to reconnect the remote components with the main network. 5. Discussions In this work we used six approaches to evaluate network damage: the number of disrupted road links, the number of components, the ratio of network lengths, the number of cut off people, index Vt developed by Yin and Xu (2010) and its modification (Vtp) by taking into account the number of inhabitants living in each node. The problem is that when evaluating network damage no single measure alone is able to describe the full extent of network destruction. 5.1. Limitation of indices and further recommendations for impact assessment First, we should scrutinize the indices which provide information about the performance of the entire network. The network efficiency indices Vt and Vtp inform about the decline of the network serviceability but lack any other important information, e.g. the number of cut-off people or number of components into which the network broke apart. The ratio of network lengths informs about the range of the damage caused by the event but has the same disadvantages of the efficiency indices. In addition, all three indices are not homogeneously distributed over the network region considered, i.e. they depend on the size of the network. For example, the impacts in Ústecky´ region (ULK) caused by the August 2010 event were primarily in the north of the region. The Vt value indicated a decrease in the serviceability of the network (Vt = 0.065, see Table 2) but it is clear that the event had no impact in most of the region (no damage, Vt = 0.0), whereas the northern part of the ULK region
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Fig. 9. ULK in August 2010. The event affected only the northern part of the region. The Vt values would differ significantly if they were computed for the affected part only. The lack of alternative paths beyond the region on the north was due to presence of a state border.
was affected seriously. If we limit the analysis only to this part as shown in Fig. 9, the index rises significantly (Vt = 0.29) and the decrease in the serviceability is comparable to the Zlín region in 1997. We therefore strongly suggest using the same regions (the same networks) when comparing impacts of various disruptive events in a given area. The reason is that the values of the indexes influenced by actual region borders and therefore computing indices only for the impacted part of an area will inevitably lead to confusing results. The other three indices – the number of disrupted road links, the number of components and the number of cut off people – provide us with more detailed information about the impact of the event but are unable to express how the networks perform after the events. None of the indices indicate which roads must be repaired to reconnect the network. They also say nothing about the remoteness of the newly created components, i.e. whether they lie in a neighborhood of a main component or whether it is necessary to reconnect another component to get access to some set of components. This information is extremely important for planning reconstruction efforts which are usually based upon the number of cut-off people. This information can be obtained from component analysis, as was performed for the ZLK 1997. From this perspective it is therefore obvious that the impacts of disasters to road networks have to be evaluated by more than one index to gain a richer picture of the consequences of an event. 6. Conclusions In this paper we provided the analysis and description of several events caused by natural hazards in the Czech Republic between 1997 and 2010 based upon six measures which offer different types of information about damages. We selected only such events which had significant impacts in terms of simultaneously interrupted road links. We mentioned the limitations of all indices and pointed out that using the indices together can provide a much truer picture of the respective events. We chose such indices which include only one characteristic of the damaged network to avoid the loss of information typical for many indices, which is caused by adding together several numbers representing respective characteristics. In addition, the indices used must also enable measurement of damages in broken networks. We argue that this is the only way to get a comprehensive view of the impacts. From the results obtained here, we conclude that the worst situation
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occurred in 1997, specifically in the Zlín region. The reason was not only the extent of the damage, but also the shape and structure of the ZLK road network, which is influenced by mountainous topography. Acknowledgments This paper was prepared with the help of a project undertaken by Transport R&D Centre (OP R&D for Innovation No. CZ.1.05/2.1.00/03.0064) and project ‘Quantification of the risk to the transport infrastructure of the Czech Republic by natural hazards’, (No VG20102015057), supported by the Ministry of the Interior of the Czech Republic. We also thank to two anonymous reviewers for their valuable comments. References Albert, R., Jeong, H., Barabási, A.L., 2000. Error and attack tolerance of complex networks. Nature 406. Anbazhagan, P., Srinivas, S., Chandran, D., 2012. Classification of road damage due to earthquakes. Nat. Hazards 60, 425–460. Arcidiacono, V., Cimellaro, G.P., Infuso, A., 2012: Road network resilience assignment methodology. 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Contents lists available at ScienceDirect
Transportation Research Part A journal homepage: www.elsevier.com/locate/tra
Evaluating road network damage caused by natural disasters in the Czech Republic between 1997 and 2010 Michal Bíl ⇑, Rostislav Vodák, Jan Kubecˇek, Martina Bílová, Jirˇí Sedoník CDV Transport Research Centre, Líšenˇská 33a, Brno 636 00, Czech Republic
a r t i c l e
i n f o
Article history: Received 20 October 2014 Received in revised form 8 July 2015 Accepted 14 July 2015 Available online 15 August 2015 Keywords: Road network Network efficiency index Network damage Natural disasters Vulnerability Czech Republic
a b s t r a c t Road networks play a vital role in maintaining a functioning modern society. Many events perceptibly affect the transport supply along these networks, especially natural disasters such as floods, landslides, and earthquakes. Contrary to more common disruptions of traffic from accidents, or maintenance closures, natural disasters are capable of destroying large numbers of roads and usually cover vast areas. When evaluating network damage no single measure alone is able to describe the full extent of network destruction. In this study, we investigated six highly damaging natural disasters, which occurred in the Czech Republic between 1997 and 2010. They were all induced by extreme rainfall or by rapid snowmelt and resulted in floods and landslides. Their impacts are evaluated with respect to the damage to road networks and decreased serviceability. For mutual comparison of the impacts and their analysis we used several criteria, described in the paper, related to economic impacts, physical harm to individuals and infrastructures, and the effects on connectivity and serviceability. We also introduced a new measure based on the network efficiency index which takes into account the importance of nodes based on their population. Moreover, we provide a detailed analysis of one such event in July 1997 that significantly affected the road network of the Zlín region. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Damage to road networks by natural disasters Natural disasters (e.g. floods, landslides or earthquakes) are frequent causes of road network damage. Compared with other common traffic disruptions, such as traffic accidents and maintenance closures, these natural events may completely destroy transport infrastructure in a given area and cause the long-term cut-off of inhabitants from the main network (Eleutério et al., 2013), as well as appreciable economic losses (e.g. Anbazhagan et al., 2012). Well-known events which have seriously impacted road networks include the Loma Prieta earthquake which hit the San Francisco Bay area in 1989, the 1994 Northridge earthquake in the Los Angeles metropolitan area, and the 1995 disaster in the Kobe region (Chang and Nojima, 2001). The common feature was serious damage to the road network, specifically the highways. A comprehensive overview of road damages due to earthquakes and their classification is presented by Anbazhagan et al. (2012). Besides such exceptional disasters there are others which are caused primarily by heavy rains (and subsequent floods or landslides).
⇑ Corresponding author. Tel.: +420 548 641 795; fax: +420 548 423 712. E-mail address: [email protected] (M. Bíl). http://dx.doi.org/10.1016/j.tra.2015.07.006 0965-8564/Ó 2015 Elsevier Ltd. All rights reserved.
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These produce rather minor overall damage but may also disrupt the road network within a large region (e.g. Vinet, 2008; Hilker et al., 2009). 1.2. Road networks and their resistance to incidents Road networks can be depicted as a specific kind of communication network represented by graphs. This allows one to study the consequences of various events on their. The events can be caused consciously as a form of intentional attack or unconsciously as natural disasters (see Albert et al., 2000; Dall’Asta et al., 2006). In the second case the events contains certain form of randomness. In this work we pay attention to the second type of events. The most studied problems cover the concepts of vulnerability and robustness of a road network infrastructure (e.g. Murray and Grubesic, 2007; Matisziw et al., 2009; Reggiani, 2013). The term ‘robustness’, from the view of the whole road network and its ability to ensure the accessibility of an area, refers to its capability to absorb a certain amount of disrupted links (Berdica, 2002). A robust network should include a certain amount of link redundancy, so that a small disruption would not lead to collapse, defined as a system-wide decline into several disconnected parts. However, there are some limitations on why real road networks cannot have maximal robustness. The problem is that the more robust the network, the more redundant it is. It means that such a network will be more expensive and demanding of maintenance. Moreover, road networks are significantly influenced by the relief topography, which may sometimes become a dominant factor in determining their structure (Rodrigue et al., 2010). At the opposite extreme, the most vulnerable or ‘least robust’ (see Berdica, 2002) network will disintegrate into two parts (in graph theory called components, e.g. Newman, 2010) after any link is taken away. Mountain valleys are often weakly connected with the rest of a network and the disruption of one or two links often leads to a complete cut-off of nearby inhabitants. Thus, the aim of a vulnerability analysis is to identify those critical links in a network (e.g. Bell, 1999; Berdica, 2002; Jenelius et al., 2006; Sohn, 2006). It is important to say that network vulnerability is not dependent on probability; it represents the consequences of an event (see Berdica, 2002). It follows from the definitions of robustness and vulnerability of road networks that both concepts are fundamental for the analysis of consequences of natural events. Two features of natural disasters are important to note. First, such natural events are characterized by some randomness in their occurrence. Second, the events can affect the most vulnerable links in the network and thus maximize their impact. Moreover, new weak links may emerge as a result of partial network damage which are necessary for the proper performance of the rest of the network. 1.3. Measuring the network damage To obtain any information about the robustness and vulnerability of road networks and about the impact of natural events it is necessary to establish some suitable measures. When measuring the impact of a disaster, overall economic losses are generally used for comparison. A loss of connection and reduced accessibility is often a result of such catastrophes, however. Comparison of pre- and post-disaster network performance is therefore possible using suitable indices connected with robustness. There are numerous studies which estimate and measure impacts of various natural disasters on infrastructure, including roads. When evaluating damage caused by a disaster, direct losses are usually computed (e.g. overall damage to infrastructure). From the view of network performance the indirect losses may be also important (Yee et al., 1996). Versini et al. (2010) evaluated the vulnerability of roads in connection with flooding on the basis of geographic information and actual flooded road segments over the last 40 years in the area around Gard, France. The impact of the earthquake in Haiti on the accessibility of humanitarian aid was summarized by Bono and Gutiérrez (2011). They applied GIS spatial analysis to show changes in accessibility for the affected towns. Chang and Nojima (2001) evaluated the traffic system performance for the city of Kobe, which was affected by an earthquake in 1995 and compared it with antecedent earthquake events in the USA (Loma Prieta in 1989 and Northridge in 1994). Their study used a ratio of the lengths of damaged and undamaged road networks. They also used an accessibility ratio which is based on distance in computation of the length of a path between two nodes. When the network is broken up into two and more components, however, their measure stretches to infinity, because it is impossible to find finite paths among nodes from these components, and the ratio is therefore unusable. Another shortcoming of previously published methods is that they compute changes from one simultaneously closed network link (e.g. Jenelius et al., 2006). This could be still used when modeling the effect of traffic accidents or the planned closure of a link. However, natural disasters are capable of damaging many roads at one time. This means the information we have about the current state of a network and flows in it (see for instance Louail et al., 2015; Gallotti and Barthelemy, 2015; Lenormand et al., 2014a,b) are dramatically changed. The common traffic pattern (Gottlich and Klar, 2009; Lammer et al., 2006; Helbing, 2002, 2001) completely disappears and the standard traffic control begins to be useless. The state of the transportation system also differs significantly from common traffic congestions (Treiber et al., 2000) and therefore is not in equilibrium (Kurauchi et al., 2009). This is the reason why there is a need to take a different view of the network after certain events which result in the disintegration of the network. Thus it is also necessary to analyze the resilience of the network (see Cimellaro et al., 2010; Arcidiacono et al., 2012).
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However, some of the methods, which were originally developed and used for analysis of the impact of several closed links, can be used or modified for natural disasters (e.g. Sohn, 2006). Other suitable methods for evaluation of damage to the entire network can be found in other fields, especially network science. Yin and Xu (2010) introduced a network efficiency index, which is capable of evaluating a disintegrated network; one that is breaking up into many separated parts or components. The index is based upon the indices developed in Latora and Marchiori (2004). Such a measure is therefore suitable when comparing pre- and post-disaster road network performance. One potential improvement to this index can be found in Dangalchev (2006), where the influence of longer detours is reinforced. The aim of this work is to demonstrate the impacts of natural disasters which affected the Czech Republic (CZ) between 1997 and 2010, from a perspective of the road network performance and overall damage. The work is organized as follows: Data, its collection and database preparation is presented in Section 2. The methods used for network damage evaluation are described in Section 3. Section 4 presents the results which are further discussed in Section 5.
2. Data 2.1. Natural disaster events Forms of road damage can be characterized by the following three levels: Total destruction, when the road embankment has to be reconstructed. Partial damage, when the road section is also closed, but the only subsequent work involves repairs to the road surface or minor stabilization of the road embankment. Closure due to temporal flooding or sedimentation (e.g. of mud from a field). This type of interruption does not require almost any repairing work. In this study we focused on the first two types of road closures, which require reconstruction and are usually long lasting. The road sections belonging to the third case may be opened to traffic in few hours and thus they are not important for our study. For this reason we also ruled out two disaster events connected with the transition of the deep low pressure storms known as Kyrill (January 2007) and Emma (March 2008), which resulted in many interrupted roads due to tree fall, but no significant road damage.
2.2. GIS data The Czech Road and Motorway Directorate provided a shapefile of the Czech road network. The data in this file is topological. The data on the number of inhabitants and the location of individual buildings were provided by the Czech Statistical Bureau. The shapefile of the road network which was used for the network analysis contains a simplified geometry where every link is a straight line and individual links are connected in nodes which are in the form of junctions. Nevertheless, the network topology is preserved. The attributes of the links include the real length of each segment. Analyses were performed for whole regions in order to assess the changes in accessibility among individual towns and villages. Therefore, the data do not include the street networks in towns and villages. Every town and village is represented by a node. In the case of larger towns, located on opposite sides of river banks, they may be represented by two or more nodes. Data were processed in GIS software ArcGIS 10.1 (for the preparation of road networks for other analyses), Scilab (for the computation of indices and components). Figures were created using CorelDRAW Graphics Suite X5.
2.3. Database on road section damage We produced a database of road sections damaged or closed due to natural events in the Czech Republic. Similar databases have also been compiled in other countries (e.g. Hilker et al., 2009; Papagiannaki et al., 2013). In the first phase we prepared and sent questionnaires to local road network administrators to indicate places and dates where disruption or damage to a road section occurred due to a natural disaster. This work started in 2011 and focused on the period between 1997 and 2010. As of May 2013, our database of affected road sections had 2752 records. By using exact dates of the interruptions for the road sections, we were able to delimit areas which were affected by the same event. Due to the fact that natural processes such as local floods or landslides occur quite frequently, we set a limit for concurrently interrupted road sections to define a network-wide important event. This limit (41 roads) is an average number of closed road sections (for any reason) in the whole CZ road network per day. It was derived from the on-line system of traffic information (www.dopravniinfo.cz). This number does not contain information on interrupted streets within built areas of cities and towns.
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2.4. An overview of the main natural disasters since 1997 The following storm and flood events were used in this study to assess impacts on transportation networks.
2.4.1. July 1997 This event occurred as a result of five days of precipitation (July 4–8) which reached 433 mm and exceeded the monthly average for July by nearly four times (Krejcˇí et al., 2002). The consequence was the most intense flood of the last 100 years, especially on the Morava River. Due to the geological conditions in the eastern part of the Czech Republic which is formed by landslide-susceptible flysch rocks, hundreds of landslides occurred. Many of them damaged residential houses, roads and railways.
2.4.2. August 2002 Within the 6–8th and again the 9–13th of August 2002, two deep cyclones passed through Central Europe (Ulbrich et al., 2003). An area of the Czech Republic was struck by the tail of these storms. Both moved slowly and therefore the rainfalls were long-lasting. Notably the second cyclone whose center moved directly over the western part of the Czech Republic caused extreme precipitations (Hladny´ et al., 2005; Kaspar and Müller, 2008). Between the 6 and 15th of the August up to 450 mm of precipitation fell.
2.4.3. April 2006 The winter of 2005/2006 was exceptional in terms of a very thick snow cover. This snow stayed until the end of March when higher air temperatures and heavy rainfall appeared, due to changes in air mass circulation over Europe. The first significant rain fell on March 26, which was followed on March 28–29 by further rains. This period yielded up to 35 mm of rainfall. The consequence was major flooding throughout the Czech Republic and more than 100 landslides in Moravia (Bíl and Müller, 2008; Klimeš et al., 2009).
2.4.4. June 2009 For Central Europe it is typical for air masses to circulate generally from the west to the east. It is more unusual for moist and warm air to flow to the Czech Republic from the east, especially during the summer. These events are often connected with intense storms. This type of circulation occurred at the turn of June and July 2009. This event was special due to its exceptionally long duration of almost two weeks (22th June–4th July), whereas a normal duration is 3–4 days. It was the longest period with this type of circulation for the last 63 years. In two meteorological stations precipitation exceeded 120 mm/2 days, in four others it exceeded 60 mm/h and in two others it exceeded 30 mm/15 min (MZP, 2009). The discontinuous area affected by this event (see Fig. 3) resulted in multiple isolated storms which caused extensive damage.
2.4.5. May 2010 Extreme precipitation occurred in the second part of May and at the beginning of June 2010 in the broader area of Central Europe. Watersheds were already saturated by an unusually wet May and were not able to accommodate another rainfall. The event can be divided into two phases between 15–20th of May and 30th May–3th June. At some stations rainfall topped 100 mm in 6–8 h. In the affected areas, three-day precipitation exceeded 80 mm, and some saw as much as 300 mm. Floods and landslides were also registered (Pánek et al., 2011).
2.4.6. August 2010 Two episodes with convectional rainfalls within 6–8th and 13–15th of August 2010 caused extreme floods in the north-western part of the Czech Republic. Maximal daily precipitation was about 180 mm, while the three days total (between 6 and 8th) reached 300 mm (Kubát et al., 2010).
3. Methods We used several metrics for analyzing a network undergoing some kind of disruption.
3.1. The number of broken or damaged road links The overall number of damaged road links is usually well known and may be used in absolute and relative numbers to all the road links. It is therefore possible to state the relative impact of an event and compare it to events on other networks with different size.
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3.2. The ratio of network lengths This index was used by Chang and Nojima (2001) and compares lengths of a network before and after a disaster. If a road link is broken, it is no longer available for transport and therefore its entire length, regardless the extent of the actual damage, is not taken into computation. 3.3. Network components In the case of exceptionally damaging natural disasters, a large number of links may be disrupted and the network would disintegrate into several components. The number of components and their size also show the impact of natural disasters (Fig. 1). 3.4. The number of people cut off from the main road network If we know the number of inhabitants for each node, we may also find out how many people likely remained cut off from the main network in individual components. From a practical point of view the main concern should be the number of people that remained cut off. We express both the absolute number of people affected by road disruption and a ratio to overall population within the respective region. 3.5. Network efficiency index To evaluate the disruption of a damaged network, we use an approach based upon the closeness centrality (e.g. Newman, 2010). This approach compares the disrupted network’s average efficiency (index Et) with the average efficiency of an undamaged network (index E) and provides us information about the network efficiency Vt given by the relation (see Yin and Xu, 2010)
Vt ¼
E Et E
where
E¼
X1 1 NðN 1Þ i–j dij
ð1Þ
1
and Et ¼
2
nodes s
X 1 1 NðN 1Þ i–j dij
1
ð2Þ
2
nodes s
where N is number of nodes and dij and dij represent the shortest path (in terms of number of links) between a node pair (i, j) in the undamaged and damaged network, respectively. Relation (1) is in fact a modification of the importance of a node from Latora and Marchiori (2004). The corresponding value of Vt is within the interval [0, 1] and measures a drop in network performance (or network serviceability, see Berdica, 2002) if some type of disruption occurs (Fig. 2). The importance of the Vt consists in its ability to describe the performance of the entire network, including separated parts (components). 3.6. Weighed network efficiency index Index Vt has one disadvantage. It cannot depict the importance of the individual nodes. This importance can be measured by the people living in the nodes (see Taylor et al., 2006). Thus we suggest a modification of (1) which looks as follows:
V tp ¼
Ep Etp Ep
ð3Þ
where
Ep ¼
X Pi Pj 1 NðN 1Þ i–j dij
"
2
people
2
nodes s
# and Etp ¼
X Pi Pj 1 NðN 1Þ i–j dij
"
2
people
2
#
nodes s
ð4Þ
Fig. 1. Examples of possible impacts of two simultaneously disrupted links (L). In the first case (A) one cut-off component (C) with six nodes (N) will emerge, in the second case (B) two cut-off components, each with only one node emerges.
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Fig. 2. An example of Vt computed for two types of interruption on a hypothetical network. In the first case (A) Vt = 0.056338, in the second (B) Vt = 0.2647887. This number is also possible to read as degree by which the serviceability of the network was reduced (by 5.6% or by 26% respectively).
Pi represents the number of people living in node i. In fact, it can be said that the importance of the shortest path between nodes i and j is directly proportional to the number of people living in nodes i and j and inversely proportional to the length of this path. This modification of the index can also be understood as a simple incorporation of a travel demand into our calculation. This enables us to measure the efficiency of the network under the assumption that the travel demand is not changed after the event. This is not always a realistic assumption because it is impossible to estimate a change in travel demand after such an event. However, we use both indices to analyze the impact of the event. We assume that they measure extreme cases which may appear, i.e. the case when the travel demand remains unchanged and the case when there is no travel demand and all nodes have the same importance. We refer the reader to Crucitti et al. (2006) for modification of (1) in case of geographical analysis. The methods used differ in computational-time demand. While the simplest method which evaluates the absolute numbers of broken links or their ratios into unbroken links is easy to derive within a GIS, the network-based methods including Vt and Vtp required from tens of minutes up to several hours. A topological structure of the networks had also been kept to allow for the shortest path algorithms. 4. Results 4.1. Extent and economic impact of the natural disasters On the basis of the data on road disruptions (see Section 2.3) we generated a map with the extents of the six natural disasters (see Section 2.4) which affected the road network of the Czech Republic between 1997 and 2010 (Fig. 3). The real extent of the areas with extreme precipitation may slightly differ, but for the delimitation of the events the recorded disruption of road links was substantial. In 1997, the most affected areas were in the eastern part of the Czech Republic, whereas in 2002 it was the western part. The event in 2006 had the largest spatial extent. The 2009 event had a discontinuous area of road disruption. In 2010, the first event struck the eastern part of the Czech Republic while the second event struck the northeastern part. We adjusted the published economic losses in relation to known inflation and to planned expenses of the state budget. Without these corrections we could get erroneous results which would overestimate impacts of the newest events (e.g. Barredo, 2009). In human and economic costs, the most devastating event was the 1997 event (see Table 1); 60 people died and after taking inflation into account, direct costs exceeded 100 billion (109) CZK. This was about 11% of the planned income of the state budget in the same year (Table 1). The 1997 event was also the first large flood which struck the Czech lands after a long period with little flooding. The last recorded floods of the same extent in the area were recorded at the turn of 19th and 20th centuries (Brázdil and Kirchner, 2007). The 1997 event was therefore exceptional in size and magnitude and nearly unprecedented. As such, there were no functional and tested crisis plans and warning systems. Another large flood hit the western part of the Czech Republic in August 2002. The losses were significantly lower despite the fact that the affected area was larger (49% vs. 41%) and that Prague, the Capital, was flooded as well. Also, fatalities were one third of those that occurred in 1997. The gradual progress of floods in 2006 and better readiness contributed to the fact that the losses from these were lower, though still 7 billion CZK. The series of isolated flash floods in 2009 hit 36% of the Czech Republic and resulted in 9 billion CZK loses. In May 2010, the floods, which were not extensive (only 13.5% of the Czech Republic) caused a relatively large amount of damage (5 billion CZK). It was the third event when landslides occurred in significant numbers and damaged roads. In August 2010, an area in the northern part of the Czech Republic was hit by devastating floods. Losses computed to area units were comparable to those in 1997. It hit only 4% of the Czech Republic, but the overall losses were 10 billion CZK. 4.2. Impact evaluation of the road networks from the view of regional administrative units Due to the fact that the roads (excluding highways and first class roads) are managed by local administration units (regions) and due to the extreme computation demands for determining indexes Vt and Vtp we evaluate the impacts of natural disasters in regional networks. To keep the network intact and prevent what might appear to be artificial dead-end links,
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Fig. 3. Delimitation of the six most important natural disasters was made on the basis of recorded damage to roads.
Table 1 Extent and impacts of natural disasters since 1997. Year, month
Extent (km2/% area CZ)
Overall losses in 109 CZK
Losses per unit area (109 CZK/km2)
Ratio of losses to planned income of the state budget (%)
Losses to transport infrastructure (109 CZK)
Disrupted road links
Fatalities
1997, 2002, 2006, 2009, 2010, 2010,
32,607/41.3 38,442/48.7 47,644/60.4 28,324/35.9 10,698/13.5 3312/4.2
102.4 89.4 6.9 8.7 5.2 10.1
3.14 2.33 0.14 0.31 0.49 3.05
11.40 10.60 0.68 0.76 0.50 0.98
19.6 11.6 2.5 3.9 1.9 3.2
300 174 137 141 108 129
60 19 9 15 3 5
7 8 4 6 5 8
All losses were computed in Czech crowns (26 CZK 1 €) and inflation was taken into account according to data provided by the Czech National Bank (www.cnb.cz).
we kept the existing detour routes beyond the borders of the regions. The results, ordered according to index Vt, are shown in Table 2. The worst of the affected areas in almost all parameters was the Zlín region (ZLK) in July 1997. Index Vt shows that ZLK road network serviceability was reduced by almost 30% in July of 1997. When taking into account the number of people in the nodes the Vtp was almost 33%. The ratio of networks lengths (L) drop to 78.4%. The second and the third most damaged regions according to Vt were Moravskoslezsky´ region (MSK) and Olomoucky´ region (OLK), both also in July 1997. The serviceability of their networks was lowered by about 10%. The other parameters between the two regions differed significantly: MSK 1997 was hit in places where relatively few people lived (1.3%) in contrast to OLK (6.1%). This is also supported by the Vtp values. The network of MSK was disintegrated into 32 components which resulted in 40 cut off nodes, whereas OLK fell apart into only 14 components but with 107 nodes off the main network. The results for OLK 1997 are also interesting because a relatively few disrupted road links (2.7%) caused the cut off of quite a large number of nodes (7.4%). In the rest of the regions and events this ratio was usually reversed. For the entire set of regions (in Table 2) a drop in serviceability by more than 5% was recorded in only 7 cases. In the rest of the 19 cases the Vt was between 0.004 and 0.037 (0.4–3.7% decrease). When considering people in nodes, Vtp, the situation remains quite similar to Vt with two exceptions: Jihocˇesky´ region (JHC) 2002 and MSK 1997 (Fig. 4). In JHC 2002 only 0.3% people were cut-off, but paths among the inhabited nodes were
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M. Bíl et al. / Transportation Research Part A 80 (2015) 90–103 Table 2 Impacts of natural disasters on regional road networks. Region
ZLK MSK OLK ZLK LBK JHC ULK JMK LBK MSK ULK ZLK JHC OLK PAK KVK JMK PAK ZLK OLK JHC STC ULK OLK MSK JMK a
Year
1997 1997 1997 2010 2010 2002 2010 2006 2009 2010 2002 2006 2006 2009 2006 2002 2009 1997 2009 2006 2009 2002 2009 2010 2009 2010
Month
7 7 7 5 8 8 8 4 7 5 8 4 4 6 4 8 7 7 6 4 7 8 7 5 7 5
Vt
0.30 0.10 0.10 0.09 0.09 0.08 0.07 0.04 0.04 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00
Vtp
0.33 0.05 0.08 0.09 0.06 0.18 0.06 0.02 0.04 0.01 0.03 0.03 0.01 0.01 0.02 0.01 0.01 0.02 0.02 0.02 0.00 0.01 0.01 0.00 0.00 0.00
Damaged links Abs.
%
121 98 52 28 39 91 68 24 21 39 34 14 38 20 37 10 34 20 5 13 15 30 14 9 10 13
13.1 6.4 2.7 3.0 3.2 3.2 3.0 1.1 1.7 2.6 1.5 1.5 1.3 1.0 1.9 1.1 1.5 1.0 0.5 0.7 0.5 0.5 0.6 0.5 0.7 0.6
La
78.4 88.9 95.2 95.3 94.8 95.2 94.5 97.9 97.6 94.2 97.3 97.7 97.5 97.6 96.7 97.5 97.8 98.0 99.7 98.7 99.3 99.2 98.6 99.0 98.6 98.8
Components
47 32 14 11 12 18 19 4 4 7 11 5 7 8 4 4 5 5 2 4 3 4 3 1 2 1
Cut off population Abs.
%
67,442 17,418 44,245 16,932 11,112 1996 8042 2844 1126 2862 3491 2470 284 5665 452 935 843 876 280 2479 38 610 340 0 228 0
11.3 1.3 6.1 2.8 2.6 0.3 0.9 0.2 0.3 0.2 0.4 0.4 0.0 0.8 0.1 0.3 0.1 0.2 0.1 0.3 0.0 0.1 0.0 0.0 0.0 0.0
Ratio of broken and unaffected networks after Chang and Nojima (2001).
Fig. 4. The relation between Vt and Vtp. It is clear that Vt alone cannot give a true picture in a situation when inhabitants are distributed unevenly within a network or when damaged roads were important for traffic. The term importance means here that the road is a part of an optimal route between nodes.
seriously affected and therefore the index’s rise was based on the relative elongation of important paths among those heavily populated nodes (see Fig. 5). Whereas in JHC 2002 the road network was not impacted to a large extent, in MSK 1997 the road network (network topology) was damaged seriously. Roads connecting localities with few or no people were predominantly affected or blocked.
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Fig. 5. The road situation in JHC 2002, where only 0.3% of the people were cut-off and also Vt was only 7.9. Due to the fact, that the main roads lying on the shortest paths among the largely inhabited areas were affected (see the damaged roads in the central part of JHC around heavily populated nodes), the Vtp raised to 18.0.
4.3. Zlín region in July 1997 As was stated above (Table 2), the ZLK region in 1997 was the worst affected region of those we studied. In order to illustrate our method of analysis, we will depict the impacts of this event in detail. As a result of floods and landslides the road network of ZLK broke up into 46 separate components. At first it was difficult to connect the separated parts of the area. Urgent medical cases were secured by the air rescue service. Helicopters provided drinking water and food. The most damaged road segments were repaired only provisionally with procedures such as temporary bridging. In total 121 of the 923 links were disrupted (13.1%). Some of them were disrupted in more than one part, but the majority of them were disrupted in one locality. The total length of these disrupted links was 452 km. This is not the total length of the road in question, but the length of the links which were disrupted anywhere between two nodes. The main component was formed of 641 nodes out of the total number of 723 (which formed 89% of the intact network). The other components had substantially fewer nodes. The largest one of them (component No. 2, see Fig. 6) had 13 nodes and the others had between 1 and 7 nodes. There were 9 components with 2 nodes and 32 components had only one node (Fig. 7). Regarding the number of inhabitants, the situation was slightly different. The majority of the inhabitants were located within the main component. There were 528,211 inhabitants, which also constituted 89% of all 595,653 inhabitants of the Zlín region. The second largest number of inhabitants was located in component No. 15 (10,031 inhabitants), which was formed by a single node – a part of the town of Uherské Hradišteˇ near the Morava River (Fig. 7). At that time the town was divided into 3 parts and separated from the rest of the network. The second largest component with 13 nodes was located in the eastern part of the region and contained 6168 inhabitants (see Fig. 8, component No. 2). We also analyzed locations of the components relative to the main component. This is important when there is a need to reconnect the network. To access 38 out of 46 components from the main component just one link needed repair. The other 8 components, however, were located ‘behind’ other components. They were reachable through two (6 cases) or even three (2 cases) damaged links (see components No. 30 and 35, Fig. 8). This example occurred in the closed mountain valley in the spring area of the Vsetínská Becˇva River.
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Fig. 6. The situation in ZLK 1997.
Fig. 7. The road network of ZLK around the town of Uherské Hradišteˇ disintegrated in July 1997 into four components. The town itself was divided into three main parts. The largest one contained about 10,000 people.
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Fig. 8. ZLK 1997 – the eastern part of the region, where many components originated, and from which two (No. 30 and 35), were separated from the main network by 3 disrupted links.
It means that the term component may refer to a different degree of remoteness, determined not only by the pure distance from the main network in meters but also by a number of broken links which have to be repaired before the component can be reached. We can thus determine the minimal number of steps (in terms of repaired road sections), which are necessary to reconnect the remote components with the main network. 5. Discussions In this work we used six approaches to evaluate network damage: the number of disrupted road links, the number of components, the ratio of network lengths, the number of cut off people, index Vt developed by Yin and Xu (2010) and its modification (Vtp) by taking into account the number of inhabitants living in each node. The problem is that when evaluating network damage no single measure alone is able to describe the full extent of network destruction. 5.1. Limitation of indices and further recommendations for impact assessment First, we should scrutinize the indices which provide information about the performance of the entire network. The network efficiency indices Vt and Vtp inform about the decline of the network serviceability but lack any other important information, e.g. the number of cut-off people or number of components into which the network broke apart. The ratio of network lengths informs about the range of the damage caused by the event but has the same disadvantages of the efficiency indices. In addition, all three indices are not homogeneously distributed over the network region considered, i.e. they depend on the size of the network. For example, the impacts in Ústecky´ region (ULK) caused by the August 2010 event were primarily in the north of the region. The Vt value indicated a decrease in the serviceability of the network (Vt = 0.065, see Table 2) but it is clear that the event had no impact in most of the region (no damage, Vt = 0.0), whereas the northern part of the ULK region
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Fig. 9. ULK in August 2010. The event affected only the northern part of the region. The Vt values would differ significantly if they were computed for the affected part only. The lack of alternative paths beyond the region on the north was due to presence of a state border.
was affected seriously. If we limit the analysis only to this part as shown in Fig. 9, the index rises significantly (Vt = 0.29) and the decrease in the serviceability is comparable to the Zlín region in 1997. We therefore strongly suggest using the same regions (the same networks) when comparing impacts of various disruptive events in a given area. The reason is that the values of the indexes influenced by actual region borders and therefore computing indices only for the impacted part of an area will inevitably lead to confusing results. The other three indices – the number of disrupted road links, the number of components and the number of cut off people – provide us with more detailed information about the impact of the event but are unable to express how the networks perform after the events. None of the indices indicate which roads must be repaired to reconnect the network. They also say nothing about the remoteness of the newly created components, i.e. whether they lie in a neighborhood of a main component or whether it is necessary to reconnect another component to get access to some set of components. This information is extremely important for planning reconstruction efforts which are usually based upon the number of cut-off people. This information can be obtained from component analysis, as was performed for the ZLK 1997. From this perspective it is therefore obvious that the impacts of disasters to road networks have to be evaluated by more than one index to gain a richer picture of the consequences of an event. 6. Conclusions In this paper we provided the analysis and description of several events caused by natural hazards in the Czech Republic between 1997 and 2010 based upon six measures which offer different types of information about damages. We selected only such events which had significant impacts in terms of simultaneously interrupted road links. We mentioned the limitations of all indices and pointed out that using the indices together can provide a much truer picture of the respective events. We chose such indices which include only one characteristic of the damaged network to avoid the loss of information typical for many indices, which is caused by adding together several numbers representing respective characteristics. In addition, the indices used must also enable measurement of damages in broken networks. We argue that this is the only way to get a comprehensive view of the impacts. From the results obtained here, we conclude that the worst situation
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occurred in 1997, specifically in the Zlín region. The reason was not only the extent of the damage, but also the shape and structure of the ZLK road network, which is influenced by mountainous topography. Acknowledgments This paper was prepared with the help of a project undertaken by Transport R&D Centre (OP R&D for Innovation No. CZ.1.05/2.1.00/03.0064) and project ‘Quantification of the risk to the transport infrastructure of the Czech Republic by natural hazards’, (No VG20102015057), supported by the Ministry of the Interior of the Czech Republic. We also thank to two anonymous reviewers for their valuable comments. References Albert, R., Jeong, H., Barabási, A.L., 2000. Error and attack tolerance of complex networks. Nature 406. Anbazhagan, P., Srinivas, S., Chandran, D., 2012. Classification of road damage due to earthquakes. Nat. Hazards 60, 425–460. Arcidiacono, V., Cimellaro, G.P., Infuso, A., 2012: Road network resilience assignment methodology. 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