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Risk Analysis to Extreme Rainfall: A retrospectiveapproach
Desireé E. Villalta, Lelys I. Bravo de Guenni, Andrés M.Sajo-Castelli, José M. Campos
CEsMA - Universidad Simón BolívarCaracas-Venezuela
June 16�26 2014PASI 2014, Buzios, Brasil
IntroductionHazard Model
Vulnerability ModelRisk Model
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Presentation Outline
1 Introduction
2 Hazard Model
3 Vulnerability Model
4 Risk Model
5 Future Work
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Introduction
1 Present a retrospective analysis in where hazard, vulnerabilityand exposure are modeled using historical data during theperiod 1970�2006.
2 Model vulnerability, hazard and risk including uncertainty in allits components.
3 Describe a framework for risk mapping and present anapplication for Vargas state, Venezuela.
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Reported events and People a�ected: South America1960�2000
Source: Data from the Center for Research on the Epidemiology of Disasters (www.cred.be)
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Population Exposure: South America 1960�2000
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1 Extreme weather continues to preoccupy society with hugesconcerns on public safety and economic loses.
2 Attention has focused on global climate change and potentialintensi�cation on the water cycle elements as precipitation andriver discharge.
3 It is the conjunction of geophysical and socioeconomic factorsthat shapes human sensitivity and risk to extreme weatherevents (Pielke and Sarewitz, 2005).
4 Several de�nitions of vulnerability and risk are available in thesocial and physical science literature. Working de�nitions areneeded for modeling purposes.
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Important concepts
Natural Hazard (H)
It is a natural phenomenon (Storm, Volcanic Eruption, Earthquake,etc.) causing damage to a population, ecosystem or unit of concern.This damage might potentially cause a disaster, when the levels ofdamage go beyond the response capability of the a�ected unit.
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Important concepts
Vulnerability (V)
Downing et al. (1999) de�nes vulnerability as the degree of loss(from 0 to 100%) in human casualties, property damage orinterruption of an economic activity due to a damaging event on agiven period and location.
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Important concepts
Exposure (E)
It is the amount of infrastructure, population, ecosystem orenvironmental unit exposed to single or multiple hazards.
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Important concepts
Risk (R)
Risk is de�ned as the expected losses due to a damaging event. Itis the combination of the amount of damage caused for a particularhazard with the probability associated to this particular hazard.Normally is written as R = E ∗ V |H ∗ P(H).
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SREX IPCC ReportManaging the Risk to Extreme Events and Disasters (2012)
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SREX Report De�nitionsIPCC, 2012
Exposure: The presence of people; livelihoods; environmentalservices and resources; infrastructure; or economic, social, orcultural assets in places that could be adversely a�ected.
Vulnerability: The propensity or predisposition to be adverselya�ected.
Disaster Risk: The likelihood over a speci�ed time period ofsevere alterations in the normal functioning of a community ora society due to hazardous physical events interacting withvulnerable social conditions, leading to widespread adversehuman, material, economic, or environmental e�ects thatrequire immediate emergency response to satisfy critical humanneeds and that may require external support for recovery.
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SREX Report De�nitionsIPCC, 2012
Probabilistic Risk Analysis
De�nes risk as the product of the probability that some event (orsequence) will occur and the adverse consequences of that event.
Risk = ProbabilityxConsequence
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General Framework
We de�ne the components of Risk following Downing et al. (1999)Notation: For a given time t and location s, we de�ne:
Ht,s : Hazard (Rainfall anomalies in mm).
Vt,s : Vulnerability or Loss Function (Number of PeopleA�ected per 100,000 inhabitants).
Rt,s : Risk (Expected number of people a�ected).
Et,s : Exposure (Total population × 100,000 inhabitants).
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General Framework
The expected loss conditioned on Ht,s can be de�ned as
E [Vt,s |Ht,s ].Et,s
Finally Risk is de�ned as follows:
Risk
EH [EV |H [Vt,s |Ht,s ].Et,s ] = Et,s .
∫H
EV |H [Vt,s |Ht,s ].P(Hs,t)dH
We will be integrating out the above equation with respect to theHazard Hs,t and its Posterior Predictive distribution P(Hs,t).
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General Framework
The expected loss conditioned on Ht,s can be de�ned as
E [Vt,s |Ht,s ].Et,s
Finally Risk is de�ned as follows:
Risk
EH [EV |H [Vt,s |Ht,s ].Et,s ] = Et,s .
∫H
EV |H [Vt,s |Ht,s ].P(Hs,t)dH
We will be integrating out the above equation with respect to theHazard Hs,t and its Posterior Predictive distribution P(Hs,t).
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We model the total number of people a�ected per 100, 000inhabitants as a function of a set of co-variables as columns ofthe matrix X .
We used reported counts of people a�ected for the period1970�2006 by extreme rainfall related events. The values areaggregated counts on a monthly basis for the study region.
Since we have an important presence of zero values (monthswith no events) or events with no casualties, we used azero-in�ated regression to model vulnerability.
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Let Y1, . . . ,Yn be the observed values of the number of peoplea�ected due to an extreme rainfall event for a particular time t,t = 1, . . . , n. Assuming the values of Yt are independent, we havethe Zero-In�ated Poisson model:
Zero-In�ated Poisson Regression (ZIP)
Yt =
0 with probability pt + (1− pt)e
−λt
k with probability (1− pt)e−λt λkt
k!
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Let Y1, . . . ,Yn be the observed values of the number of peoplea�ected due to an extreme rainfall event for a particular time t,t = 1, . . . , n. Assuming the values of Yt are independent, we havethe Zero-In�ated Poisson model:
Zero-In�ated Poisson Regression (ZIP)
Yt =
0 with probability pt + (1− pt)e
−λt
k with probability (1− pt)e−λt λkt
k!
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Poisson mean vector λ = (λ1, . . . , λn) satis�es
log(xTλ) = Bβ
x is the exposure vector of size n.
Probability parameter vector p = (p1, . . . , pn) satis�es
logit
(p
1− p
)= Gγ
G and B are covariate matrices, not necessarily sharing the samecovariates. β and γ are unknown parameters.
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Another extension is the Zero In�ated Negative Binomial model
Zero-In�ated Negative Binomial Regression (ZINB)
Yt =
0 with probability pt + (1− pt)
θθ
(λt + θ)θ
k with probability (1− pt)Γ(k + θ)
Γ(θ) k!
λkt θθ
(λt + θ)k+θ
with mean λt , shape parameter θ, and Γ(·) the Gamma function.
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Another extension is the Zero In�ated Negative Binomial model
Zero-In�ated Negative Binomial Regression (ZINB)
Yt =
0 with probability pt + (1− pt)
θθ
(λt + θ)θ
k with probability (1− pt)Γ(k + θ)
Γ(θ) k!
λkt θθ
(λt + θ)k+θ
with mean λt , shape parameter θ, and Γ(·) the Gamma function.Villalta Guenni Sajo Campos Risk Mapping
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A Hierarchical Bayesian Kriging model was �tted to monthlyrainfall data of 27 locations from years 1970�2006 following Leand Zidek (2006).
The Sampson and Guttorp method is used to considernon-stationarity conditions in the spatial covariance matrix.
Posterior predictive simulations of total rainfall are obtainedfor each month, year and location in where rainfall data isestimated.
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Monthly Rainfall Totals at ungauged (u) and gauged (g) locations
Yt =(Y
(u)t ,Y
(g)t
), t = 1, . . . , n. Assuming Yt are independent
Yt | zt ,B, Σ ∼ Np (ztB, Σ)
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zt = (z1t , . . . , zkt) is a k-dimensional vector of covariables.
B =(B(u) B(g)
)is a (k × p) matrix of regression coe�cients,
where p = u + g .
B and Σ are assumed to have conjugate priors: B |Σ has akp-dimensional Multivariate Normal and Σ has anp-dimensional Inverse-Wishart distribution.
Given the hyperparameters de�ning the distributions of B andΣ, the joint posterior predictive distribution of
Yf =(Y
(u) ′
f Y(g) ′
f
)conditional on the covariate vector zf is
fully characterized as the product of two Student'st-distributions, for 1 ≤ f ≤ n.
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Monitoring Stations
Meteorological stations (INAMEH) 2013Quantity: 2469
Active: 1276
Retired: 1193
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Particular case: Vargas state
−67.4 −67.2 −67.0 −66.8 −66.6 −66.4
10.4
010
.45
10.5
010
.55
10.6
010
.65
Stations of Vargas state, Venezuela
Longitude
Latit
ude
●●
●
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●
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●
●
● ●
●
●
●
●
●
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●
●
●
● ●50045006
0503
5045
9313
5016
0422
5020
5044
05021401
1414
5001
5042
1439
1501
1413
1504
9311
50415043
0508
9304
1404
1412
5005 5011
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Vargas state
−67.4 −67.2 −67.0 −66.8 −66.6 −66.4 −66.2
10.3
510
.45
10.5
510
.65
longs
lats
1
2
3
4
5
6
7
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161
162
163
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166
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168
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2
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167
168
123 4
5
6
7 89
10
1112 1314 15
16 17 18
19202122 232425
26272829
3031
3233
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Station Data
Year
Available data
100% 50% 0%
1900 1920 1940 1960 1980 2000
LA GUAIRA−ESTACION G.F.G
PUERTO CRUZ−PANARIGUA
PETAQUIRE
EL LIMON−OFICINA
LA GUAIRA−ELECTRICIDAD
HACIENDA OSMA
MAMO−PLANTA
MARAPA
MAMO−ESTANQUE
CAOMA−PLANTA
LA GUITARRITA
MAIQUETIA
EL CARITE
LAS MERCEDES
MAIQUETIA−AEROPUERTO
MACUTO
PUERTO CRUZ
PUERTO ORICAO
LA PENITA
ANARE
NAIGUATA
PUERTO CHICHIRIVICHE
HACIENDA NARANJAL
URIA
CARUAO
CHUSPA
LOS CARACAS
TODASANA
MAMO
CARAYACA
CARABALLEDA
LOS CARACAS−FILA DEL INDIO
LOS CARACAS−EL LIMON
CARUAO
ORITAPO
OSMA
MARIA ISABEL
CATIA LA MAR
PIEDRA AZUL 1
PIEDRA AZUL 2
PIEDRA AZUL 3
MAMO−ESCUELA NAVAL
PETAQUIRE−DIQUE
NAIGUATA−ESTANQUE
LOS CORALES
USB−CAMBURI GRANDE
1
2
3
4
5
6
7
8
9
10
11
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13
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22
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35
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37
38
39
40
41
42
43
44
45
46
Longevity of stations (VA)
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Station Data
Available years of data
1960 1970 1980 1990 2000 2010
Year
Longevity of stations
1 URIA (5004)
2 ANARE (5006)
3 MAIQUETIA−AEROPUERTO (0503)
4 PIEDRA AZUL 2 (5045)
5 HACIENDA NARANJAL (9313)
6 LOS CARACAS−EL LIMON (5016)
7 CATIA LA MAR (0422)
8 MARIA ISABEL (5020)
9 PIEDRA AZUL 1 (5044)
10 MAIQUETIA (0502)
11 MAMO (1401)
12 LAS MERCEDES (1414)
13 CARABALLEDA (5001)
14 ORITAPO (5042)
15 EL CARITE (1439)
16 TODASANA (1501)
17 LA PENITA (1413)
18 CHUSPA (1504)
19 CARAYACA (9311)
20 CARUAO (5041)
21 OSMA (5043)
22 MACUTO (0508)
23 PUERTO ORICAO (9304)
24 PUERTO CRUZ (1404)
25 LA GUITARRITA (1412)
26 NAIGUATA (5005)
27 LOS CARACAS (5011)
Station
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Station Data
Jan Mar Mar Jul Sep Nov
020
040
060
080
010
00Station Los Caracas (5011)
Pre
cipi
tatio
n (m
m)
Jan Mar Mar Jul Sep Nov
020
040
060
080
010
00
Station Puerto La Cruz (1404)
Pre
cipi
tatio
n (m
m)
Jan Mar Mar Jul Sep Nov
020
040
060
080
010
00
Station Naiguatá (5005)
Pre
cipi
tatio
n (m
m)
Jan Mar Mar Jul Sep Nov
020
040
060
080
010
00
Station La Guitarrita (1412)
Pre
cipi
tatio
n (m
m)
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Hierarchical Kriging ModelVariogram �t in the Dispersion space (D-space)
D plane coordinates Exponential Variogram
−6 −4 −2 0 2 4 6
−1
.0−
0.5
0.0
0.5
1.0
x
y
12
3
4
5
6
7
8
9
1011
12
13 14
15
16
17
18
19
20
21
22
23
24
25
26 27
0 5 10 150.
00.
51.
01.
52.
0D−plane distance
Disp
ersio
n
Exponential Fitted Variogram
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Naiguata station (5005)
Jan Feb Mar
mm
1950 1960 1970 1980 1990 2000 2010
01
00
20
03
00
40
0
Post. prob. sim. prec. (5%, 95%) interval for January
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
mm
1950 1960 1970 1980 1990 2000 2010
01
00
20
03
00
40
05
00
60
0
Post. prob. sim. prec. (5%, 95%) interval for February
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
mm
1950 1960 1970 1980 1990 2000 2010
01
00
20
03
00
40
0
Post. prob. sim. prec. (5%, 95%) interval for March
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
Apr May Jun
mm
1950 1960 1970 1980 1990 2000 2010
02
00
40
06
00
Post. prob. sim. prec. (5%, 95%) interval for April
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
mm
1950 1960 1970 1980 1990 2000 2010
05
01
00
15
0
Post. prob. sim. prec. (5%, 95%) interval for May
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
mm
1950 1960 1970 1980 1990 2000 2010
05
01
00
15
02
00
Post. prob. sim. prec. (5%, 95%) interval for June
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
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Naiguata station (5005)
Jul Aug Sep
mm
1950 1960 1970 1980 1990 2000 2010
05
01
00
15
02
00
25
0
Post. prob. sim. prec. (5%, 95%) interval for July
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
mm
1950 1960 1970 1980 1990 2000 2010
05
01
00
15
02
00
Post. prob. sim. prec. (5%, 95%) interval for August
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
mm
1950 1960 1970 1980 1990 2000 2010
05
01
00
15
02
00
Post. prob. sim. prec. (5%, 95%) interval for September
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
Oct Nov Dec
mm
1950 1960 1970 1980 1990 2000 2010
02
00
40
06
00
80
01
00
0
Post. prob. sim. prec. (5%, 95%) interval for October
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
mm
1950 1960 1970 1980 1990 2000 2010
01
00
20
03
00
40
05
00
Post. prob. sim. prec. (5%, 95%) interval for November
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
mm
1950 1960 1970 1980 1990 2000 2010
01
00
20
03
00
40
05
00
60
0
Post. prob. sim. prec. (5%, 95%) interval for December
Station: NAIGUATA (5005) [grid.id=83, cat.id=16, mat.col=194]
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La Guitarrita station (1412)
Jan Feb Mar
mm
1950 1960 1970 1980 1990 2000 2010
01
00
20
03
00
40
0
Post. prob. sim. prec. (5%, 95%) interval for January
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
mm
1950 1960 1970 1980 1990 2000 2010
01
00
20
03
00
40
05
00
60
0
Post. prob. sim. prec. (5%, 95%) interval for February
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
mm
1950 1960 1970 1980 1990 2000 2010
05
01
00
15
02
00
25
03
00
35
0
Post. prob. sim. prec. (5%, 95%) interval for March
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
Apr May Jun
mm
1950 1960 1970 1980 1990 2000 2010
01
00
20
03
00
40
05
00
60
0
Post. prob. sim. prec. (5%, 95%) interval for April
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
mm
1950 1960 1970 1980 1990 2000 2010
05
01
00
15
02
00
25
03
00
Post. prob. sim. prec. (5%, 95%) interval for May
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
mm
1950 1960 1970 1980 1990 2000 2010
05
01
00
15
02
00
25
03
00
Post. prob. sim. prec. (5%, 95%) interval for June
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
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La Guitarrita station (1412)
Jul Aug Sep
mm
1950 1960 1970 1980 1990 2000 2010
05
01
00
15
02
00
25
0
Post. prob. sim. prec. (5%, 95%) interval for July
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
mm
1950 1960 1970 1980 1990 2000 2010
05
01
00
15
02
00
25
03
00
35
0
Post. prob. sim. prec. (5%, 95%) interval for August
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
mm
1950 1960 1970 1980 1990 2000 2010
05
01
00
15
02
00
25
0
Post. prob. sim. prec. (5%, 95%) interval for September
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
Oct Nov Dec
mm
1950 1960 1970 1980 1990 2000 2010
01
00
20
03
00
40
0
Post. prob. sim. prec. (5%, 95%) interval for October
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
mm
1950 1960 1970 1980 1990 2000 2010
01
00
20
03
00
40
05
00
60
0
Post. prob. sim. prec. (5%, 95%) interval for November
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
mm
1950 1960 1970 1980 1990 2000 2010
01
00
20
03
00
40
05
00
Post. prob. sim. prec. (5%, 95%) interval for December
Station: LA GUITARRITA (1412) [grid.id=139, cat.id=7, mat.col=193]
Villalta Guenni Sajo Campos Risk Mapping
IntroductionHazard Model
Vulnerability ModelRisk Model
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Vulnerability Model
Number of events and people a�ected in the period 1970�2009
1970 1977 1984 1991 1998 2005
Num
ber
of e
vent
s
05
1015
2025
30
1970 1977 1984 1991 1998 2005
Tota
l num
ber
of a
ffect
ed
050
000
1000
0015
0000
2000
0025
0000
3000
00
Villalta Guenni Sajo Campos Risk Mapping
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Vulnerability Model for Vargas state
Response Variable y : Number of Casualties.
Model formula: y ∼ x1 + . . .+ xp | z1 + . . .+ zq.
x1, . . . , xp: covariables included in the count model.
z1, . . . , zq: covariables included in the zero-in�ation model.
Model AIC ZIP AIC ZINB p-Value Voung Test(ZIP vs. ZINB)
1 y ∼ MEI | 11 3141 322 0.0122 y ∼ MEI+ PRECIP | 1 2490 309 0.020
Number of zeros explained by model 2 ZINB: 414/451 (92%).1A �1� means an intercept with no covariates has been used for the
zero-in�ation model.Villalta Guenni Sajo Campos Risk Mapping
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Casualties vs. Rainfall
0 100 200 300 400
010
2030
40
Index
sqrt
(Cas
ualti
es)
Casualties vs. Precipitation
Real data Predicted data
Year
Pre
cipi
tatio
n (m
m)
1970 1980 1990 2000
020
040
060
080
0
Villalta Guenni Sajo Campos Risk Mapping
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Vulnerability Maps
Persons
0
5
10
Persons
0
5
10
Villalta Guenni Sajo Campos Risk Mapping
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Risk Maps
Persons
0
5
10
Villalta Guenni Sajo Campos Risk Mapping
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1 This is work in progress. We apologize...
2 Changes of exposure with time were accounted for, butchanges of exposure with space were not. This can beimproved with higher resolution population data sets.
3 Uncertainty in the Vulnerability model parameters needs to beincluded in the model structure.
4 To estimate Risk we really need integration with respect toP(Vt,s ,Ht,s), the joint probability distribution of Hazard andVulnerability.
5 A fully Bayesian modeling approach will be implemented.
Villalta Guenni Sajo Campos Risk Mapping
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References
Downing, T.E.; Olsthoorn, A.J. and Tol, R.S.J. (eds.) 1998.Climate, Change and Risk. Rouledge, New York.
Pielke Jr R.A. and Sarewitz D. 2005 Bringing society back intothe climate debate. Popul. Environ. 26,255�268.(doi:10.1007/s11111-005-1877-6)
Villalta, D.; Bravo de Guenni, L. and Sajo-Castelli, A. 2014.Risk Analysis to Extreme Rainfall: A retrospective approach (InPrep.).
Vörösmarty, C.J; Bravo de Guenni, L.; Wollheim, W.M.;Pellerin, B.; Bjerklie,D.; Cardoso, M.; D'Almeida, C.; Green, P.and Colón, L. 2013. Extreme Rainfall, Vulnerability and Risk: acontinental scale assessment for South America. Phil Trans RSoc A.371:20120408.
Villalta Guenni Sajo Campos Risk Mapping
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Thanks for your attentionVillalta Guenni Sajo Campos Risk Mapping
