Davos Maposa 2014-IDRC14

If the data is
sufficiently tortured,
it will confess.
Estimating high quantiles of extreme flood
heights in the lower Limpopo River basin of
Mozambique using model based Bayesian
5th International Disaster and Risk Conference IDRC 2014
‘Integrative Risk Management - The role of science, technology & practice‘ • 24-28 August 2014 • Davos • Switzerland
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approach
Daniel Maposa, Monash University, South Africa;
James Cochran, University of Alabama, USA;
‘Maseka Lesaoana, University of Limpopo, South Africa.

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Introduction
• Floods have recently become a common natural disaster in
Southern Africa and other parts of the world.
• This paper pays attention to extreme floods in Mozambique; a
developing and emerging nation, Limpopo River Basin where
the February 2000 floods claimed the lives of more than 700
people and caused economic damages estimated at
US$500million.
• Limpopo River Basin is characterised by extreme natural
hazards.
• Recently in 2013 two women gave birth on rooftops in
Chokwe district (Jackson, 2013)

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Introduction
• Source: AFP/Ussene Mamudo, January 2013

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Motivation
• A substantial amount of money that has been originally
designated for development get diverted to relief and
rehabilitation assistance to disaster affected people each
year a disaster occurs.
• IFRC claims that aid money buys 4 times as much
humanitarian impact if used before a disaster than on
post-disaster relief operations.
• It is hoped that this study will help reduce the associated
risk & mitigate the deleterious impacts of these floods
on humans and property.

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Materials and Methods
• The data used in this study was obtained from the
Mozambique National Directorate of Water (DNA).
• Daily flood height data series (in metres) over the period
1951-2010 for the lower Limpopo River at Chokwe
hydrometric station was used. The raw data consist of
instantaneous daily river flows recorded at least once a day.
• Sequential steps were taken to select the highest peak flood
in each hydrological year, resulting in a sample of size 60
allowing the use of block maxima approach.
• Rainfall cycle: October-April; Dry season, May-September

F D(G )  2  and corresponding normalisation sequences of
3    That is, the
M b
  
k , m m
  ( ), as 
 
P G x m
9 (Fisher and Tippett, 1928; Coles,
a 
12       .


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Probability framework of block maxima
We consider independent and identically 1 distributed (i.i.d.) random variables (Xi )i1 with
common distribution function
0
constants ( 0) m a  and ()nb such that lim ( ) ( ), . m
m m
m
F a b F x x 

distribution function F satisfies the extreme value condition with index or equivalently F 4
belongs to the domain of attraction of G 5 (Fisher and Tippett, 1928; Coles, 2001; Dombry,
2013). We divide the sequence of i.i.d. random variables 1 ( )i i X  6 into blocks of length m 1
and we define the th k block maximum by , ( 1) 1 max( ,..., ), 1 k m k m km M X X k   7   (Coles,
2001; Dombry, 2013). For a fixed m 1, the variables , 1 ( ) k m k M  8 are i.i.d. with distribution
function m F and
0
m
10 2001; Dombry, 2013; Maposa et al., 2014). The extreme value distribution with index  is
11 given in Coles (2001), Dombry (2013) and Maposa et al. (2014) as
    1/
G (x) exp 1 x , , 1 x 0
   

Time series plot of annual daily maximum flood
heights at Chokwe hydrometric station (1951-2010)
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Parameter estimation
• Table 1: MLE estimates of the GEV parameters
Parameter Estimate Standard Error 95% *CI
4.26452 0.25374 (3.7574;4.7723)
1.78893 0.17725 (1.4343;2.1436)
-0.08351 0.07273 (-0.2290;0.0620)
• Table 2: Bayesian estimates of the GEV parameters
Parameter Estimate Standard Error 95% *CI
4.27235 0.00602 (3.7636;4.7872)
1.90141 0.00484 (1.5565;2.4002)
-0.06824 0.00184 (-0.2027;0.1046)







In-sample evaluation of estimated tail quantiles at
Return period ML estimate
*(Exceedances)
Bayesian
estimate
*(Exceedances)
95th 0.05 20 years 8.97 m (1) 9.38 m (1)
98th 0.02 50 years 10.22 m (1) 10.79 m (1)
99th 0.01 100 years 11.10 m (1) 11.78 m (1)
99.5th
200 years
250 years
11.92 m (1)
12.18 m (1)
12.72 m (1)
13.02 m (0)
99.8th 0.002 500 years 12.94 m (1) 13.90 m (0)
99.9th 0.001 1000 years 13.65 m (0) 14.74 m (0)
99.99th 0.0001 10 000 years 15.76 m (0) 17.27 m (0)
Quantiles Exceedance
probability (p)
99.6th
0.005
0.004
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different probabilities
*Exceedances in brackets represent the number of sample observations above the estimated flood level (quantile).

Return level plot of posterior distribution with 95% Bayesian
credible intervals (dashed lines) at Chokwe hydrometric station
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Added value for the Post 2015 Framework for
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Disaster Risk Reduction
• How did your work support the implementation of the Hyogo
Framework for Action:
– Helps reduce the associated risk & mitigate the deleterious impacts of
floods on humans and properties e.g. bridges, houses, factories etc.
– Contributes towards a reduction in the amount of aid money spent on
post-disaster relief operations.
– Advancement of research in developing countries: Mozambique warrants
attention as one of the least developed flood-prone countries.
• From your perspective what are the main gaps, needs and further
steps to be addressed in the Post 2015 Framework for Disaster Risk
Reduction in
– Research: Forecasting and monitoring of natural hazards
– Education & Training: More training workshops, seminars and conferences
on natural hazards
– Implementation & Practice: Recommendations from natural disaster
experts should be taken seriously by national and local governments.
– Policy: Introduce more Disaster Risk Reduction, Resilience and
Management courses in colleges and universities

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References
• Maposa, D., Cochran, J.J. and Lesaoana, M. (2014). Estimating high quantiles of extreme floods in the
lower Limpopo River of Mozambique using model based Bayesian approach. Natural Hazards and Earth
System Sciences, Discussions, 2:5401-5425. doi:10.5194/nhessd-2-5401-2014.
• Maposa, D., Cochran, J.J. and Lesaoana, M. (2014). Investigating the goodness-of-fit of ten candidate
distributions and estimating high quantiles of extreme floods in the lower Limpopo River basin,
Mozambique. Journal of Statistics and Management Systems (forthcoming). www.tandfonline.com/tsms
• Dombry, C. (2013). Maximum likelihood estimators for the extreme value index based on the block
maxima method. ArXiv: 1301.5611v1 [math.PR], available at: http://arxiv.org/pdf/1301.5611.pdf (last
access: 17 August 2014).
• Ferreira, A. and de Haan, L. (2013). On the block maxima method in extreme value theory. ArXiv:
1310.3222v1[math.ST], available at: http://arxiv.org/pdf/1310.3222.pdf (last access: 17 August 2014).

Davos Maposa 2014-IDRC14

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