Vulnerability analysis in Complex Networks under a Flood Risk Reduction point of view
Leonardo B. L. Santos, Tanishq Garg, Aurelienne A. S. Jorge, Luciana R. Londe, Regina T. Reani, Roberta B. Bacelar, Igor M. Sokolov
VVulnerability analysis in Complex Networks under a FloodRisk Reduction point of view
Leonardo B. L. Santos* , Tanishq Garg , Aurelienne A. S. Jorge , Luciana R. Londe ,Regina T. Reani , Roberta B. Bacelar , Igor M. Sokolov Centro Nacional de Monitoramento e Alertas de Desastres Naturais (Cemaden), S˜aoJos´e dos Campos, Brazil Humboldt University of Berlin, Germany Indian Institute of Technology Kharagpur, Kharagpur, India Instituto Nacional de Pesquisas Espaciais (INPE), S˜ao Jos´e dos Campos, Brazil Anhanguera College, Sao Jose dos Campos/SP, Brazil* [email protected]
Abstract
The measurement and mapping of transportation network vulnerability to naturalhazards constitute subjects of global interest, especially due to the climate change, andfor a sustainable development agenda. During a flood, some elements of atransportation network can be affected, causing loss of life of people and damage tovehicles, streets/roads, and other logistics services - sometimes with severe economicimpacts. The Network Science approach may offer a valuable perspective consideringone type of vulnerability related to network-type critical infrastructures: the topologicalvulnerability. The topological vulnerability index associated with an element is definedas the reduction on the network’s average efficiency due to the removal of the set ofedges related to that element. We present a topological vulnerability index analysis forthe highways in the state of Santa Catarina (Brazil), and produce a map consideringthat index and the areas susceptible to urban floods and landslides. The risk knowledge,combining hazard and vulnerability, is the first pillar of an Early Warning System, andrepresent an important tool for stakeholders from the transportation sector in a disasterrisk reduction agenda.
In a scenario of global change, some climatic and extreme weather events are expectedto increase in frequency and intensity and cause more social and economic impacts inseveral sectors, such as transportation systems and urban mobility. As presented inseveral papers in literature, the cost for repairing transport assets after either an urbanflood or landslide represents a significant percentage of the total damage cost of severalrecent disasters around the world (Doll et al. , 2014; Pregnolato et al. , 2017; Eidsvig etal. , 2017; Santos et al. , 2017a; Koks et al. , 2019).To mitigate those impacts, it is necessary to evaluate the risk associated withdisasters and the best ways to deal with them. “Disaster risk reduction is aimed atpreventing new and reducing existing disaster risk and managing residual risk, all ofwhich contribute to strengthening resilience and therefore to the achievement ofsustainable development” (UNDRR, 2017).December 23, 2020 1/9 a r X i v : . [ phy s i c s . s o c - ph ] D ec or disaster risk reduction, vulnerability is a key concept. There are several typesand meanings for vulnerability. According to Wisner et al. (1994), vulnerabilityrepresents “the characteristics of a person or group and their situation that influencetheir capacity to anticipate, cope with, resist and recover from the impact of a naturalhazard (an extreme natural event or process)”. The UN Office for disaster riskreduction also includes assets and systems as subjects to vulnerability: “The conditionsdetermined by physical, social, economic and environmental factors or processes whichincrease the susceptibility of an individual, a community, assets or systems to theimpacts of hazards” (UNDRR, 2017).In the transportation systems’ literature, there are also different meanings forvulnerability (Schlogl et al. , 2019). Berdica (2002) suggested that network vulnerabilityshould be understood as “susceptibility to incidents that can result in considerablereductions in road network serviceability”. Taylor et al. (2006) understood networkvulnerability as the extent of a failure to impact the original purpose of the system.Vulnerability is a key idea in network science as well. Due to its generality forrepresenting the system topology (relation among the elements on the system), NetworkScience approaches have been applied to a huge number of very different areas(Newman, 2010; Estrada, 2011; Barab´asi, 2016). Recently, Mattsson & Jenelius (2015),Arosio et al. (2018) and Santos et al. (2019b) discussed interfaces between ComplexSystems Science and Disaster Science. However, the first one did not apply its ideas inany real case study, the second one did not analyse the topological vulnerability index,and the third one did not show any susceptibility map, just the topological vulnerabilityindex itself.This paper presents a formulation for a vulnerability index based on efficiencies ofthe system of networks. It aims to locate the most vulnerable links in a transportationnetwork and to assess whether these links are susceptible to hazards and disruptions.The idea is presented as a case study on a set of highways, which are mapped based onvulnerability index and disaster susceptibility data. Brazil is among the ten countries most affected by weather-related disasters in the last20 years (UNISDR, 2017). Santa Catarina state, located in the Brazilian Southernregion, is particularly affected by disasters - there is an annual mean of 64 damagerecords triggered by hydrological processes, such as floods in Santa Catarinamunicipalities (UFSC, 2016). The maximum value was achieved in 2008, when thematerial losses summed almost 1 billion US Dollar (UFSC, 2016).According to the last census track (2010), there are 295 municipalities and morethan 6 million inhabitants in the state. The State’s HDI - Human Development Index -is 0.774 and it is the third in the Brazilian HDI ranking (IBGE, 2010). Despite the highsocio-economic indicators for municipalities from Santa Catarina state, there are manycommunities at risk in those places due to characteristics of land occupation (Londe etal. , 2014; Londe et al. , 2015). The mountainous relief in the east side determined thehuman settlement in the fluvial plains, which are areas naturally prone to floods.Moreover, industrialization and economic growth attracted many people to the regionsand induced interventions in the environment, such as deforestation, landfill andirregular constructions (Londe et al. , 2014; Londe et al. , 2015).The susceptible flood areas used in this study were mapped by the BrazilianGeological Survey (CPRM), based on a database of previous occurrences and in situ evaluation of physical characteristics (CPRM, 2019).December 23, 2020 2/9 .2 Topological vulnerability
Several topological measures can be extracted from a network and used to analyze themodeled phenomena or processes - see Costa et al. (2007). One of these simple andimportant indexes is the shortest path length d ij between two nodes i and j , defined asthe smallest number of links from i to j , among all the possible paths between i and j .On the other hand, the efficiency e ij in the communication between nodes i and j canbe defined as inversely proportional to shortest path length between them. The averageefficiency E of the network G is defined as the average of all e ij , considering all pairs ofnodes. The topological vulnerability index of an element k in a network G , V k , is thusgiven by V k = E − E (cid:63)k E , (1)where E (cid:63)k is the efficiency of the network when the element k is inaccessible: all itsedges are removed. The first paper considering the pointwise vulnerability index wasthat of Goldshtein et al. (2004), based on two relevant previous works: Latora &Marchiori (2001) and Latora & Marchiori (2004).According to Pregnolato et al. (2016), network models are typically aspatial: theemphasis has been on topological interactions, not on their geography. Mode detailsabout space-related properties in Network Science can be found in [Barth´elemy,2011, Daqing et al., 2011].Here, we use the concept and tools of a (geo)graph, a network in a geographicalspace (Santos et al. , 2017b). Recently, this approach was applied for a mobility networkanalysis (Santos et al. , 2019a) and for a rainfall network analysis (Seron et al. , 2019). Inthis paper, we represent a set of highways as a network, calculate the topologicalvulnerability index of its elements and show them on a map. We highlight the spaciallocation of the most vulnerable element, in order to combine this information with thelocations most susceptible to either floods or landslides. Using the (geo)graph approach, we represent the set of highways as a network. For theSanta Catarina State case study area, the road network presents 1536 nodes/roadsegments and 2101 directed edges/connections between road segments.Figure 1 shows the topological vulnerability index map for all highways in the studyarea. There are 4 classes (colors in Figure 1), that corresponds to Low Vulnerability,Moderate Vulnerability, High Vulnerability, and Extremely High Vulnerability.The distribution of topological vulnerability index is highly inhomogeneous - seeFigure 2. In Figure 2, on double logarithmic scale, we show this distribution and apower lay fitting to it with an exponent as obtained by the Clauset’s method (Clauset et al. , 2009).Another important question is about where the most vulnerable elements are, inparticular, whether they are close to the areas most susceptible to floods. The four mostvulnerable segments are all on the SC-108 highway, including parts without pavement(in the rural area) and parts that cross areas susceptible to floods, in the urban area ofAnit´apolis/SC. In this city, there are several areas susceptible to floods and flash floods.Figure 3 shows the vulnerability index map for a subset of the highways in the studyarea, and, also, the areas most susceptible to hazards such as floods and landslides. Inthis subset, it is possible to see that there are some elements with high topologicalvulnerability index close to urban areas susceptible to flood. In this area, in the citiesRio Negrinho and Mafra, the BR-280 highway crosses the Negrinho River. This area isDecember 23, 2020 3/9 ig 1.
Vulnerability index map for all highways in the study area. The green color isassociated with the least vulnerable segments and the red color with the mostvulnerable ones, following a quantile-scale color legend. Bounding-box:-53.73,-29.31,-48.54,-25.98 (geographical coordinates).
Fig 2.
Distribution of values for the topological vulnerability index (black squares) anda auxiliary line (red segment) for a power law with an exponent of − . ig 3. Vulnerability index map for a subset of highways in the study area. The redcolor with the most vulnerable segments. The areas susceptible to flood are shown inblue.marked by several records of floods in the rainy season (susceptibility component),which makes traffic in the region unfeasible (impact) (UFSC, 2016).The highway BR-280 is one of the most important in Santa Catarina state, playingan important role in the transportation of goods to the ports of S˜ao Francisco do Sul,Itaja´ı and Paranagu´a. It also promotes the interconnection link between importantcities in the region, such as Joinville and Jaragu´a do Sul. Thus, there is a large flow ofpeople and goods on this highway.This representation, considering both vulnerability (as a topological index) andsusceptible areas, is an important tool for stakeholders from the transportation sector,considering climate change, disaster risk reduction and sustainable development agenda.The Risk Knowledge, combining hazard and vulnerability, is the first pillar of an EarlyWarning System (EWS) (UNDRR, 2017). Also, the transportation sector representsdirect and indirect economic losses: the first being the destruction of physical assets andthe second being a decline in economic value (UNDRR, 2017). In this work, thesuggested representation ads knowledge about the losses to the disaster risk assessment.
In this paper, we represented the set of highways from our study area as a network andcalculated the topological vulnerability index. Using the (geo) approach (Santos et al. ,2017b), it was possible to represent the results in a Geographical Information System.In our case study, in the south region of Brazil, there are some elements withvulnerability index of approximately 5%, therefore a flood impairing the traffic on thishighway’s element can reduce the efficiency of this transportation network byapproximately 5%. Also, there are elements high topological vulnerability index close toDecember 23, 2020 5/9rban flood areas, for example, in the cities of Mafra and Rio Negrinho, where theBR-280 highway crosses the Negrinho River. This area is marked by several records offloods in the rainy season (susceptibility component), which makes traffic unfeasible inthe region (impact). In the study area, the State of Santa Catarina, in Brazil, there is aheavy flow of people and goods, with some important national and international portsand airports.The topological vulnerability index associated with an element of a network (in ourcase, a highway segment) is a measure quantifying the way the system reacts to damageon this element. Although it is a measure associated with the element, the topologicalvulnerability index contains information about the dynamics throughout the wholenetwork (Santos et al. , 2019b). The disaster trigger is local but its impacts can beextended to a wider region. The topological vulnerability index captures this relationand it is possible the most important feature of this index.Accordingly to the Sendai Framework for Disaster Risk Reduction 2015-2030, one ofthe most important documents in the Disaster Risk Reduction (DRR) guidelines, thereis one global target related to “Substantially reduce disaster damage to criticalinfrastructure and disruption of basic services” (Aitsi-Selmi et al. , 2015). Many criticalinfrastructures (such as roads) are of network type, and can be modeled using theNetwork Science approach (Newman, 2010; Estrada, 2011; Barab´asi, 2016). Thetopological vulnerability index is a network measure particularly interesting in thecontext of critical infrastructures. The development of a vulnerability map to disastersand their impacts on infrastructures is aligned with the 2030 Agenda for SustainableDevelopment as well, particularly with the Sustainable Development Goals number 9, 11and 13, related to Infrastructures, Intelligent Cities and Climate (SDG, 2019).To make better urban planning and to lessen the risk of disasters, mapping riskareas is an indispensable step. This mapping can be used to create a risk reduction plan,to define priority areas for attention in the municipalities, to make recommendations forworks on infrastructure and to prepare municipal master plans. The mapping of riskareas for Santa Catarina follows the guidelines established from GIDES Project(GIDES, 2018), which is a partnership between Brazil and Japan to strengthen theNational Strategy for integrated Management of Risks and Disasters. The project’s goalis to reduce risks of disasters through non-structural preventive actions. The mainsresults are the improvement of assessment systems and risk mapping, warnings andurban planing for disaster prevention.A possible extension for this investigation is to draft risk scenarios considering othercomponents, such as the dynamic exposure (daily traffic on each highway) and otherkinds of vulnerability, for example, one based on traffic engineering parameters, or onthe coverage of meteorological sensors (Carvalho et al. , 2018).
Acknowledgments
Funding: S˜ao Paulo Research Foundation (FAPESP), Grant Number 2015/50122-0 andDFG-IRTG Grant Number 1740/2; FAPESP Grant Number 2018/06205-7; CNPq GrantNumber 420338/2018-7
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