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Université de Grenoble
PhD candidate: Davide Ceresetti
Director: Jean-Dominique CREUTINCo-director: Gilles MOLINIÉ
Université de GrenobleUniversité de Grenoble
Space-time characterization of heavy rainfall events:Space-time characterization of heavy rainfall events:Application to the Cévennes-Vivarais regionApplication to the Cévennes-Vivarais region
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Université de Grenoble
!IntroductionIntroduction
!Methodological developmentMethodological development
!Application: Severity DiagramsApplication: Severity Diagrams
!ConclusionsConclusions
OUTLINE OF THE PRESENTATIONOUTLINE OF THE PRESENTATION
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Université de GrenoblePART IPART I
INTRODUCTIONINTRODUCTION
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Context: Extreme rainfall in a Mediterranean Mountainous Region
1958-1994:
Daily amount > 190 mmTotal: 144 events
Jacq (1994)Warm humid air from Mediterranean Sea + Orography = Storms
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General overviewGeneral overview
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General overviewGeneral overviewCévennes-Vivarais: region prone to catastrophic fl ash-fl oods
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Social and economic impact (human lives, damages,...)Social and economic impact (human lives, damages,...)
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Specifi c discharge: 5-10 m3 s 1 km 2
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General overviewGeneral overview
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How can we measure the magnitude of extremes?How can we measure the magnitude of extremes?
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Is it a « hydrological monster »or a regular event?Is it a « hydrological monster »or a regular event?
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Impact of storms at various durationsImpact of storms at various durations
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Impact of storms at various durationsImpact of storms at various durations
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Aim of the studyAim of the studyHOW TO ESTIMATE THE MAGNITUDE OF RAINFALL EVENTS?
(c)19 September 2000
(a)22–23 September 1993
(b)7 September 1998
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HOW TO ESTIMATE THE MAGNITUDE OF RAINFALL EVENTS?(c)
19 September 2000(a)
22–23 September 1993(b)
7 September 1998
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NO DAMAGES NO DAMAGES 60 M€
Classic statistics are unable to detect the more dangerous event
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Need of a multi-scale descriptor of stormsNeed of a multi-scale descriptor of stormsMaximum rainfall intensity
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Integration Smoothing Trivial scale pattern
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Proposition: transform max intensity into FREQUENCYProposition: transform max intensity into FREQUENCY
SEVERITY DIAGRAMS: Event magnitude at all scalesSEVERITY DIAGRAMS: Event magnitude at all scales
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SSeverity diagrams: a storm comparison tooleverity diagrams: a storm comparison tool
(c)19 September 2000
(a)22–23 September 1993
(b)7 September 1998
Weak event Local event Heavy and extended event
DS4;ODTBU V%.%EB;4;ODTBU DANGERDANGER
Ramos et al., 2005
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Improvements proposed in the thesisImprovements proposed in the thesis
BEFORE AFTER
Size of the region 250 km2 32000 km2
Involved events Urban fl oods Flash-fl oods
Regional model
Point rainfall extremes
Spatial rainfall extremes
EMPIRICAL SCALE-INVARIANTMODEL
SPACE-TIMEMODELEMPIRICAL
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A larger regionA larger region
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Take into accountTake into accountspatial heterogeneityspatial heterogeneity
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Mediterranean Sea
Rhône River
Cévennes Massif
Geographical contextGeographical contextCévennes-Vivarais région
Size 160 x 200 km2
Elevation 0 – 1950 m
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Geographical contextGeographical contextCévennes-Vivarais région
The region gathers fl at lands , a SE oriented foothill , a mountain ridge and a plateau .
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Climatic features: average annual rainfall (mm)Climatic features: average annual rainfall (mm)
Mountain ridge:Over 2000 mm / year
Mediterranean sea shore:less than 1000 mm / year
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Measurement networkMeasurement networkOHM-CV:
OHM-CV: one of the Europe densest rain gauge networks (1/50 km2)
Cévennes- Vivarais Hydro-Meteorological ObservatoryRadar ARAMIS network Rain gauge network
Hourly (150 gauges, 1993-2008)Daily (225 gages, 1958-2000)
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Université de GrenoblePART IIPART II
METHODOLOGICAL METHODOLOGICAL DEVELOPMENTDEVELOPMENT
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ACCURATE MODELING OF EXTREMESACCURATE MODELING OF EXTREMES
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SERIES RECONSTRUCTION THROUGHSERIES RECONSTRUCTION THROUGH SCALE-INVARIANCE METHODSSCALE-INVARIANCE METHODS
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ACCURATE MODELINGACCURATE MODELING OF EXTREMESOF EXTREMES
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Dealing with ungauged scales: SCALINGDealing with ungauged scales: SCALINGSCALING OF A PROCESS
relation between probability distributions of a process at different scales
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Prerequisite: Evaluation of rain gauge uncertaintiesPrerequisite: Evaluation of rain gauge uncertainties
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Wind effect Neglectable for high intensities
Bottom hole lamination underestimation in case ofvery high intensities
Tipping-bucket device
Rain collector
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Heavy rainfall Underestimation: 5-10% 5-min rainfall 2-5 % hourly rainfall
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Reversal time: ~ 0.2 s in which no water is stored
!Experimental calibration!Numerical Simulation
Evaluation of rain gauge uncertaintiesEvaluation of rain gauge uncertainties
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Tails behaviorTails behaviorIdentifi cation of the behavior of point-rainfall extremes
```4``44`
Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
%4G77"0H
6G%H
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
??"#$
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Open question: how are the distribution tails of rainfall?
Upper bounded (Weibull)
Exponential (Gumbel)
Hyperbolic (Fréchet)
44441)24446G%H
1)24G%H
$4O''(3,'-)&4;)73-&8
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
?$"#$
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'3P/&4M()74./8'(/a4?KK@
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall modelOne has 3 possibilities:
1) Extract Maxima2) Peaks over Threshold3) Work on distributions
N&1OL&!73)'/&!76P&
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
?="#$
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At various duration --> tail behavior of point rainfall series
Ceresetti et al, 2010, WRR
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
Rigorous method
! K-S test for lower bound xmin! Estimator for power-law slope
Goldstein et al, 2004, Clauset et al., 2007L7-&
Straight line in log-log Power-law Fréchet distribution
ZS\BUQVO\
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
?#"#$
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DUAL BEHAVIOR: Need of a GENERALIZED model for EXTREMESDUAL BEHAVIOR: Need of a GENERALIZED model for EXTREMESCeresetti et al, 2010, WRR
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
Flat landsFlat lands
Mountainous regionMountainous region
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
?A"#$
Gumbel
Fréchet
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```4``44`
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
%4G77"0H
ZG%H
Construction of a scaling model for point rainfall maxima
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
?R"#$
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Menabde et al, 1999Veneziano et Furcolo, 2002
%4G77"0H
ZG%H
! " " #$%## !" " !$*
44444444444!!Z;b4G!4c//PH44444444444!!Z;b4G!4*3:H44444444444!!Z;b4G?40H
Annual Maxima Distribution is scale-invariantin the range 2 h – 1 week
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
?@"#$
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%4G77"0H
ZG%H
&" #$'%#( &" !
$'
44444444444!!Z;b4G=40H44444444444!!Z;b4G?40H44444444444!!Z;b4G!40H
4441)2E-7/4G0H
!40 ?40 =40
4441)27)7/&'8
4444[%de
b-(8'47)7/&'4Gd>!H
9/,)&*47)7/&'4Gd>?H
E0-(*47)7/&'4Gd>$H
Scaling moment linearity in log-log vs scale
! " " #$%## !" " !$*
PROBABILITY DISTRIBUTION STATISTICAL MOMENTS
Gupta et al., 1990
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
?J"#$
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Extreme distribution defi ned through moments
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
Moments scaling Extreme distribution scalingEXY9
ZG%f-H
%
R4;O_9 !4;O_ !4XSY
UBgEUOZSVO
E%SD
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
$K"#$
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall modelIDF: Intensity – Duration – Frequency curves
Q0R!S
Q0R!6!H))TUJ
8U 8!V&&W
IDF: implicit scale-invariance relations for one TR
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
$!"#$
!K4:(8
!KK4:(8
5
8
38--%;b % & '()%* "()$&
)+ "()$
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall modelIDF: Intensity – Duration – Frequency + GEV Extremes
Q0R!S
Q0R!6!H))TUJ
8U 8!V&&W8
IDF + GEV Model for all scales and all TR
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
$!"#$
!K4:(8
!KK4:(8
5
8
38--
X!GSY!H)3B6)3J
TBC
%;b % & '()%* "() $&
)+ "()$
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall modelGEV simple-scaling IDF model
X!GSY!H)3B6)3J
Q0R!S
Q0R!6!H))TUJ
8U 8!V&&W8
Use of daily series to estimate extreme rainfall down to 1 hour
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
$!"#$
*&%+,&-./ " 0$,- &-./
.)- &-./
./"!).$0"
&
&-./
$)+
.)7/&'848,31-&2
-&
"%1&-./" " 0$."
/ "!)".$)/"!).$""&
&-./
$)+
.&%.&-./
TBC
%;b % & '()%* "() $&
)+ "()$
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Need of a regional model for IDF relations
Mountainous region
Flat lands
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
$?"#$
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GEV simple-scaling IDF model: Rainfall Tr=100 years
,!U 9!U
8,!U ,>!U
ROBUST:Obtained using daily data(> 50 years of data at 225 gages)
.3L-7+7Nb13'413&*
.3L-7+7N7)+&'3-&(-*2/
Daily data hides information on infra-daily scale
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
$$"#$
Ceresetti et al, 2011, Submitted to WRR
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```4``44`
Need to model extremes in space
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
$="#$
![Page 45: Université de Grenoble Space-time characterization of ... · Université de Grenoble PhD candidate: Davide Ceresetti Director: Jean-Dominique CREUTIN Co-director: Gilles MOLINIÉ](https://reader033.vdocuments.site/reader033/viewer/2022042301/5ecbc862f2ebd94bdd0a9dcc/html5/thumbnails/45.jpg)
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
%4G77"0H
ZG%H
! " " #$%## !" " !$*
44444444444!!Z;b4G=KK4P7?H
44444444444!!Z;b4G=K4P7?H
44444444444!!Z;b4G!4P7?H
RADAR IMAGERYspatial scale-invariance
detected in the range 1-400 km2
RADAR Few events, not enough data
Solution 1: Statistics on radar data
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
$#"#$
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
Solution 2: Interpolation of point data
Signifi cant underestimation of maxima in coarse networks
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
$A"#$
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
Solution 2: Interpolation of point data
Spatial undersampling Underestimation maxima 20-50%
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
%6)O/3(&1!.6&/1 F5(&+'0/3(605!0.!'065(!)&37O+&)&5(7
$R"#$
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ARF computed from historical series 1993-2008
ARF: Areal Reduction Factor
8
OUb
O4GP7?H
Example: rainfall fi eld
" (- "2 '( $% " (- "#$( $12)3(- " 2 '( $
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
2)3%" 2
" #2!
Solution 3: Semi-empirical model based on gages
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
$@"#$
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
Solution 3: Semi-empirical model based on gages
We can build AREAL REDUCTION FACTOR
Dynamic scaling model for ARF
(
24%#5+16
Dynamic scaling ratio
De Michele et al., 2001
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
$J"#$
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ARF in Cévennes-ARF in Cévennes-Vivarais regionVivarais region
Duration has lower infl uence in mountainC+&3!HW),J
CNY
Flat Lands
?0 =0 @0 !?0 ?=0
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
=K"#$
C+&3!HW),J
CNY
Mountainous region
?0 =0 @0 !?0 ?=0
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Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall modelh
9!U Y/3(!/3517
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
=!"#$
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Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
Regional model for assessing the magnitude of extremesRegional model for assessing the magnitude of extremes
h
9!U Y/3(!/3517
Severity DiagramsSeverity Diagrams
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
=!"#$
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Université de GrenoblePART IIIPART III
APPLICATION: APPLICATION: SEVERITY DIAGRAMSSEVERITY DIAGRAMS
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Storm comparisonUse of Severity DiagramsUse of Severity Diagrams
Observed stormVirtual storm
(numerical simulation)
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
=$"#$
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From rainfall fi elds to severity diagramsFrom rainfall fi elds to severity diagrams
O(/34GP7?H
O,,+7+13'-)&4*+(3'-)&4G0H
Multi-step process involving historical series
9/5/(-':4;-32(374G:(8H
Z6)&!HUJ
U3-&423+2/4*3'3
U3*3(4*3'34)(48-7+13'/*47)*/1
%&'()*+,'-)&%&'()*+,'-)& ./'0)*)1)2-,314*/5/1)67/&'8./'0)*)1)2-,314*/5/1)67/&'8 9/5/(-':4;-32(3789/5/(-':4;-32(378 <)&,1+8-)&<)&,1+8-)&
=="#$
!%(0+)!L0)'3+6705!:01&/!&M3/O3(605!N&3/#(6)&!)056(0+65R
![Page 56: Université de Grenoble Space-time characterization of ... · Université de Grenoble PhD candidate: Davide Ceresetti Director: Jean-Dominique CREUTIN Co-director: Gilles MOLINIÉ](https://reader033.vdocuments.site/reader033/viewer/2022042301/5ecbc862f2ebd94bdd0a9dcc/html5/thumbnails/56.jpg)
Severity Diagrams computationSeverity Diagrams computation
AREAL REDUCTION FACTOR INTENSITY- DURATION- FREQUENCY
9ZOE%OV4UO%DbOVV
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Assign to each spatial rainfall observationAssign to each spatial rainfall observation a frequency value (severity)a frequency value (severity)
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Application of severity diagramsApplication of severity diagrams
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Applications: 1. Evaluation of meso-scale deterministic simulations (MesoNH)2. Evaluation of the variability of Ensemble simulations (AROME)
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Evaluation of deterministic simulations performance: 2005, Sep 06 Evaluation of deterministic simulations performance: 2005, Sep 06
Wrong Maximum Location - Rainfall Underestimation – Different space-time scalesWrong Maximum Location - Rainfall Underestimation – Different space-time scales4&+&7&((6!&(!3/[!,-88[!7O*)6((&1!(0!\CY
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Small scale max ~ 500 yrs3-4 hours / 0-100 km2
Large scale max ~ 300 yrs7-10 hours / 0-30 km2
Small scale max ~ 50 yrs3-6 hours / 0-50 km2
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Deterministic simulation performance: 2003, Dec 03 Deterministic simulation performance: 2003, Dec 03
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9-7+13'/*48/5/(-':
Maximum Severity: ~500 yrs
Time scale: 9-14 hSpatial scale: 0-200 km2
Maximum Severity: ~500 yrs
Time scale: 14-18 hSpatial scale: 200-500 km2
Severity: an effective multiscale diagnostic
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Evaluation of ensemble simulations variabilityEvaluation of ensemble simulations variability
Determine the variability of the members
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Application: effect of initial conditions Application: effect of initial conditions
Space-time scales OK, LOW magnitude
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Université de GrenoblePART IVPART IV
CONCLUSION AND CONCLUSION AND PERSPECTIVESPERSPECTIVES
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ConclusionConclusion
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PerspectivesPerspectives
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<3&4c/43661:4'0-84M(37/c)(P4')4)'0/(453(-3F1/8]
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Université de GrenobleUniversité de GrenobleUniversité de Grenoble
EXODm4_SYn
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