climate change and urban vulnerability in africa assessing vulnerability of urban systems,...

Climate change and Urban Vulnerability in Africa

Assessing vulnerability of urban systems, population and goods in relation to natural and

man-made disasters in Africa

1

“Training on the job” Course on Hazards, Risk and (Bayesian) multi-risk assessement

Napoli, 24.10.2011 – 11.11.2011

18/04/23 Fatemeh Jalayer

R = H• V • ER = H• V • E

18/04/23 Fatemeh Jalayer Slide 2

Risk assessment:

The engineering point of view

R : risk

H : hazard

V : vulnerability

E : exposure


What is hazard?

A dangerous phenomenon, substance, human activity or condition that may cause loss of life, injury or other health impacts, property damage, loss of livelihoods and

services, social and economic disruption, or environmental damage.


Risk assessment:

The engineering point of view

R = H• V • ER = H• V • E

R : risk

H : hazard

V : vulnerability

E : exposure


What is the vulnerability?

“... a human condition or process resulting from physical, social, economic, and environmental factors which determine the likelihood

and scale of damage from the impact of a given hazard“ (United Nations Development Programme, 2004)

The fraction of the total value at risk that could be lost after a specific adverse event (Principles of multi-risk assessment, EU, EUR 23615,

2009).

“... Vulnerability is the characteristics and circumstances of a community, system or asset that make it susceptible to the damaging effects of a

hazard (2009 UN International Strategy for Risk Reduction)


What is the climate change

vulnerability?

“... Vulnerability is the degree to which a system is susceptible to, or unable to cope with, adverse effects of climate change, including climate variability and extremes (United States Environmental Protection glossary for climate

change).

“... Vulnerability is a function of the character, magnitude, and rate of climate change and variation to which a system is exposed, its sensitivity, and

its adaptive capacity (United States Environmental Protection glossary for climate change).

The concept of Vulnerability seems always to involve a “system”.

The “system” is a set of interacting or interdependent components forming an integrated whole.

system

boundary

surroundings

Some general aspects of the

vulnerability

The definition of a system is very broad; it can stand for the environment, the community, the assets, the buildings, the roads and so on.


vulnerability


Technical (Physical)Vulnerability of urban structures and life-lines

EnvironmentalVulnerability of agricultureEnvironmental fragility (e.g., groundwaters, land)

SocialThe specific social inequality of people in the context of a disaster… in broad terms, how susceptible people are to a hazard

EconomicVulnerability of different economic sectors

InstitutionalEffectiveness and failure of organized structures and institutions

And hence, different types of vulnerability


A system is consisted of many components. It is not trivial to take into account the interaction of the components.


vulnerability

Vulnerability is subjected to variability:

Temporal:

• The hazard on the system can change with time

• The system can change in time.

Spatial:

• The system is usually distributed spatially.


vulnerability


vulnerability

Vulnerability assessment is usually characterized by incomplete information and its assessment is a probability-based procedure.

• Incomplete information regarding the hazard evaluation

• Incomplete information regarding the system parameters



vulnerability

The concepts of hazard, vulnerability and risk have quite a dynamic nature. What is called vulnerability from a point of view, would be called risk by some and hazard by some other at the same time and nobody is wrong!

R = H• V • ER = H• V • E


Capacity

The combination of all the strengths, attributes and resources available within a community, society or organization that canbe used to achieve agreed goals.

Capacity may include infrastructure and physical means, institutions, societal coping abilities, as well as human knowledge, skills and collective attributes such as social relationships, leadership and management.

Before to start we need the definition of capacity:


A quantitative definition for

vulnerability rooted in engineering

The vulnerability of a system or its components can be defined as the probability of its failure:

• C is the system capacity• D is the demand a system can be subjected to• C and D are attributes of the same property or

quantity (they have the same units)


What is the system demand and

how it’s related to hazard

Demand: An urgent requirement or need

Demand can be interpreted as the requirements imposed to the system by the hazard.


Linking hazard and vulnerability

In order to link vulnerability to hazard in an efficient way it is useful to introduce a variable that links hazard to system demand.

In the earthquake engineering jargon, this variable is called an intensity measure (IM).

It can be thought of as an interface variable representing the intensity of hazard .


Vulnerability and Hazard

Vulnerability can be calculated by expanding for all possible intensities of hazard:

• p(IM) represents hazard• P(D>C|IM) is called the system fragility


System vulnerability

vs Component vulnerability

The system vulnerability is a function of the vulnerability of its components. There are different ways to calculate the system vulnerability:

Employing a generalized definition of demand and capacity (the cut-set theory) for the system.

Calculating the vulnerability of the system as a function of components’ vulnerability.

Using simulation methods and calculating directly the system vulnerability.


System Reliability

The system reliability is the probability that a system it’s able to carry out a given mission. If the reliability is a time function, then it’s possible to define a mission time interval (0,t) in which the system not fails.

Structural Reliability

the concept of reliability specializes through the following assumptions:

- (0,t) is the time interval for which is designed the structure;- The reliability is the probability that the structure does not collapse;- It’s more common to talk about collapse probability than reliability.


Limit State Concept

We define failure the achievement of a state (the limit state) for which the structure is not more able to carry out a given mission.

From a mathematical point of view, the failure and the limit state are correlated by the limit state function. This function depends by the uncertainties (random variables) that involved during the structure life.

𝐺ሺ𝑋തሻ:൝> 0= 0< 0

LIMIT STATE FUNCTION

RANDOM VARIABLES

no collapsecollapse

after collapse

RELIABILITY

COLLAPSE


Demand – Capacity Approach

JOINT PROBABILITY DENSITY FUNCTION

DOMAIN Rn RANDOM VARIABLES FOR WHICH G IS NOT POSITIVE

A simple way to understand the limit state function is to divide the random variables array so to create the Demand function (D) and the Capacity function (C).

XdXpXPGPPF

Ff )()()0(



vulnerability

The Bayesian framework for inference lends itself very well to vulnerability assessment.

MXpMDp

MXDpMDXpXpD

,,

Normalizing Constant

Probability Distribution

“a posteriori”

Likelihood Function

],...,[ 1 nXXX Vector of uncertain

parametersData

DModeling

assumptions

M

Probability Distribution

“a priori”


Demand – Capacity Approach

The Cornell Reliability Index

18/04/23 Autore 25

)0()0()( GPCDPCDPPf

CDG CD )(

CDCDCDG CD 2)( 2222

)()0(G

G

G

Gf

GPGPP

11)(

G

G

G

G

G

Gf

GPP

The Cornell Reliability IndexVariation

18/04/23 Autore 26

)0(ln)1()( GPC

DPCDPPf

CDG C

Dlnlnln )(ln

CDDCCDG C

Dln2ln)(ln lnlnln

2ln

222ln

)ln

()0(lnln

ln

ln

ln

G

G

G

Gf

GPGPP

11)

ln(

ln

ln

ln

ln

ln

ln

G

G

G

G

G

Gf

GPP

The Interpretation of Cornell Reliability Index

18/04/23 Autore 27

1fP

fP 1

)1(1fP

Simulation-Based Approach

18/04/23 Autore 28

))(()()( XIEXdXpXIP FFf

F

FF PFX

PFXXI

1

1 0)(

Fsim

FF

FF

PN

PXIVOC

PXIE

1))((..

))((


Reliability

Single Component System

Series Component System

Parallel Component System


Reliability

Cut set theory

FRAGILITY(1 STRUCTURE; 1 BUILDING TYPOLOGY, K BUILDING

TYPOLOGY)


Reliability of informal settlements

To evaluate the mean annual rate of exceeding of a given flood height respect to the structural capacity height it’s necessary to calculate the follow integral:

where:

HAZARD

Is the collapse probability for a class of structures, given a specific rain height value, that can be represented as BETA distribution as below showed;

Is the mean annual rate of a given rain height, function of rain duration;



Example



Example

Fixed

3 2 1

1 2 3

Hin

ged

Hin

ged



Example

100 %100 %

75 %75 %50 %50 %25 %25 %



Class of structures

xx

yy

BUILDING TYPOLOGY IDENTIFICATION

Informal settlementsInformal settlements

Ntype,1Type,1

Ntype,2Type,2

Ntype,iType,i

Ntype,kType,k

…

…

…

…

N BuildingsN Buildings - the construction techniquesthe construction techniques - the method used for constructing the bricksthe method used for constructing the bricks - type of the mortar usedtype of the mortar used - presence or absence of lintel beamspresence or absence of lintel beams - foundation type and height from the groundfoundation type and height from the ground - the existence of drainage systemthe existence of drainage system - the material used for roof beamsthe material used for roof beams - the material used for roof coverthe material used for roof cover - type and number of openingstype and number of openings - the division of internal spacesthe division of internal spaces - possible reinforcing used in the wall cornerspossible reinforcing used in the wall corners - the techniques used for anchorage of roof inside the wallthe techniques used for anchorage of roof inside the wall - general geometrical characteristicsgeneral geometrical characteristics



Class of structures

𝑃 �𝐻𝑆𝑑 > ℎ𝑆𝑑𝐶 |ℎ𝑟𝑎𝑖𝑛൧= 𝑃 �𝐻𝑆𝑑 > ℎ𝑆𝑑𝐶 |ℎ𝑟𝑎𝑖𝑛 ,𝑇𝑦𝑝𝑒𝑖൧∙𝑃ሾ𝑇𝑦𝑝𝑒𝑖ሿ𝑘

𝑖=1 = 𝑃 �𝐻𝑆𝑑 > ℎ𝑆𝑑𝐶 |ℎ𝑟𝑎𝑖𝑛 ,𝑇𝑦𝑝𝑒𝑖൧∙𝑁𝑇𝑦𝑝𝑒𝑖𝑁𝑘

𝑖=1

( TYPE 1; TYPE 2; …; TYPE i ; …; TYPE k)

• Into TypeType ii it’s possible to study nn structures with a particular mechanical procedure trough that are recognized mm collapse (survey sampling).

• The target is to evaluate the collapse probability based on survey sampling given the information (flood height and structural typology).

h (m)h*

1 1 with probability ii

0 with probability 1 -1 - ii

Binomial distributionBinomial distribution



Class of structures

ii

iii PmnPC

mnP

PmnPmnP

|,

,

|,,| 1

Normalization factorNormalization factor

Likelihood: binomial distributionLikelihood: binomial distribution

Prior distribution: uniformPrior distribution: uniform

BETA BETA DISTRIBUTIDISTRIBUTI

ONON

For the evaluation of i it’s possible to calculate the expected value:

n

mdmnPImnE iiiii ,|,,|



Class of structuresExample

survey sampling on 1818 buildings - TYPE 1 22 collapse on 55 buildings

- TYPE 2 55 collapse on 66 buildings

- TYPE 3 33 collapse on 77 buildings

11 0.42860.4286 =0.0306=0.0306

22 0.7499 0.7499 =0.0208=0.0208

33 0.44440.4444 =0.0247=0.0247

• Expected valueExpected value

P 0.542


Reliability of a network

For the networks and lifelines, generally definable like system spatially distributed, the reliability can be obtained considering the conditions of the single part of the system (logic structure) and is function of the target that we want to achieve. Than it’s important to know:

Detailed description of the network

Position of the network respect to hazard sources

11

22 33 44

55

II11

II22

OO11

OO22

IIii Input point into the network

OOii Output point into the network

Network elementii

Element centroid

Possible direction


The network components

Roads (paved and unpaved)BridgesCritical nodesPoint of interest (e.g. schools,Emergency services, hospital)Open public concentration areasParking areasTunnelCulvertsSide drainage ditchesUnderstrains storm drainsSewage system…



Vulnerability of the single part

Functionality target

ONE to ANY

ANY to ANY



The vulnerability of a road network component can also be defined in terms of its lack of connectivity or failure:

rainrainhFF dhhpPC

DPP

rain )()1( |

• p(hrain) represents hazard

• P(D/C>1|hrain) is the component fragility

h (m)h*

1


From component to system

The system vulnerability is calculated as a function of vulnerabilities for different structural types within the system (e.g., using cutset theory).

)1min(max ij

ijF C

DPP

climate change and urban vulnerability in africa assessing vulnerability of urban systems,...

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