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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
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
!
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
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,...)
20+)3/!40516(6057
Specifi c discharge: 5-10 m3 s 1 km 2
89--!:;
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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?
Impact of storms at various durationsImpact of storms at various durations%&'()*+,'-)&%&'()*+,'-)& ./'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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Spatial and temporal scales are related
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Impact of storms at various durationsImpact of storms at various durations
Spatial and temporal scales are related
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Impact of storms at various durationsImpact of storms at various durations
Spatial and temporal scales are related
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Spatial and temporal scales are related
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Impact of storms at various durationsImpact of storms at various durations
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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Aim of the studyAim of the study
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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Improvements proposed in the thesisImprovements proposed in the thesis
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
ACCURATE MODELING OF EXTREMESACCURATE MODELING OF EXTREMES
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For a reliable magnitude estimationFor a reliable magnitude estimation
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SERIES RECONSTRUCTION THROUGHSERIES RECONSTRUCTION THROUGH SCALE-INVARIANCE METHODSSCALE-INVARIANCE METHODS
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For a reliable magnitude estimationFor a reliable magnitude estimation
ACCURATE MODELINGACCURATE MODELING OF EXTREMESOF EXTREMES
ROBUST MODELING OF EXTREMES AT VARIOUS SCALES
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For a reliable magnitude estimationFor a reliable magnitude estimation
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
```4``44`
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Evaluation of rain gauge uncertaintiesEvaluation of rain gauge uncertainties%&'()*+,'-)&%&'()*+,'-)& ./'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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Wind effect Neglectable for high intensities
Bottom hole lamination underestimation in case ofvery high intensities
Tipping-bucket device
Rain collector
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
Tails behaviorTails behaviorIdentifi cation of the behavior of point-rainfall extremes
```4``44`
Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
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Open question: how are the distribution tails of rainfall?
Upper bounded (Weibull)
Exponential (Gumbel)
Hyperbolic (Fréchet)
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
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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&
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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
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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
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Gumbel
Fréchet
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
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Construction of a scaling model for point rainfall maxima
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Menabde et al, 1999Veneziano et Furcolo, 2002
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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
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PROBABILITY DISTRIBUTION STATISTICAL MOMENTS
Gupta et al., 1990
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
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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
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall modelIDF: Intensity – Duration – Frequency curves
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall modelIDF: Intensity – Duration – Frequency + GEV Extremes
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IDF + GEV Model for all scales and all TR
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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
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GEV simple-scaling IDF model: Rainfall Tr=100 years
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Daily data hides information on infra-daily scale
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
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Ceresetti et al, 2011, Submitted to WRR
```4``44`
Need to model extremes in space
Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
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RADAR IMAGERYspatial scale-invariance
detected in the range 1-400 km2
RADAR Few events, not enough data
Solution 1: Statistics on radar data
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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
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$A"#$
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%
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ARF computed from historical series 1993-2008
ARF: Areal Reduction Factor
8
OUb
O4GP7?H
Example: rainfall fi eld
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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
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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
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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
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Tails behaviorTails behavior Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall model
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=K"#$
C+&3!HW),J
CNY
Mountainous region
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Point rainfall modelPoint rainfall model Spatial rainfall modelSpatial rainfall modelh
9!U Y/3(!/3517
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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
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Université de GrenoblePART IIIPART III
APPLICATION: APPLICATION: SEVERITY DIAGRAMSSEVERITY DIAGRAMS
Storm comparisonUse of Severity DiagramsUse of Severity Diagrams
Observed stormVirtual storm
(numerical simulation)
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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
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U3*3(4*3'34)(48-7+13'/*47)*/1
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Severity Diagrams computationSeverity Diagrams computation
AREAL REDUCTION FACTOR INTENSITY- DURATION- FREQUENCY
9ZOE%OV4UO%DbOVV
9BCBU%E_
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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\/4,3&4+8/4)+(4863,/Q'-7/47)*/14')4,)76+'/49BCBU%E_4;%OTUO.9M)(43&:48')(74),,+((-&24-&4'0/4<W5/&&/8
Applications: 1. Evaluation of meso-scale deterministic simulations (MesoNH)2. Evaluation of the variability of Ensemble simulations (AROME)
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=A"#$
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
]*7&+M&1!+365.3//
:&702^!+365.3//
SF8/(5/*48/5/(-':
9-7+13'/*48/5/(-':
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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:&702^!+365.3//
SF8/(5/*48/5/(-':
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
.)*/1N4OUS.B4S6/(3'-)&314.)*/14G.W'W)Qb(3&,/H
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?KK@a4D)5/7F/(4K!49')(7
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=@"#$
Application: effect of initial conditions Application: effect of initial conditions
Space-time scales OK, LOW magnitude
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ZBUES^9QOUS.Bi?
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ZBUES^9QOUS.Bi=
ZBUES^9QOUS.Bi#
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=J"#$
Université de GrenoblePART IVPART IV
CONCLUSION AND CONCLUSION AND PERSPECTIVESPERSPECTIVES
ConclusionConclusion
.O%D4UB9YVE9N
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#!"#$
PerspectivesPerspectives
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#?"#$
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#$"#$
<3&4c/43661:4'0-84M(37/c)(P4')4)'0/(453(-3F1/8]
Université de GrenobleUniversité de GrenobleUniversité de Grenoble
EXODm4_SYn
;-88/7-&3'-)&4)M434(-2)()+84M(37/c)(P4-&4c0-,04
(3-&M3114-848//&438434,)&'-&++74)M48,31/8
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;-88/7-&3'-)&4)M434(-2)()+84M(37/c)(P4-&4c0-,04
(3-&M3114-848//&438434,)&'-&++74)M48,31/8
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