Early-warning system (EWS) for cyclone-induced wave ...

Early-warning system (EWS) for cyclone-induced wave overtopping aided by a suite of random forest approaches

J. Rohmer1*, S. Lecacheux1, R. Pedreros1, D. Idier1, F. Bonnardot2

[email protected]: BRGM2: Direction Régionale de Météo-France pour l’Océan Indien

mailto:[email protected]

• Objective:– Probability of marine flooding (wave overtopping) as input of the

Early Warning System

– If there is overtopping,

• Magnitude of the flooding?

• Time evolution of the flooding?

EWS at Ste Suzanne

> 2






• Problem:– Computation time cost of numerical simulations too high to be

directly integrated in EWS

Problem definition

> 3






• Problem:– Computation time cost of numerical simulations too high to be

directly integrated in EWS

• What we have:

– A database of pre-calculated simulations

– ~500 synthetic cyclones

– + their impact in terms of flooding

Problem definition

> 4

Cyclone

Overtopping

N

Offshore conditions

Example of synthetic cyclone

(Quetelard and Bonnardot, Meteo

France)

> 5

Database of pre-calculated numerical results

Cyclone

Overtopping

Offshore conditions

N

Time series of offshore conditions

(Hs, Tp, SWL) offshore from

Sainte Suzanne coast

Significant Wave Height Hs


Regional wave Modellingusing WWIII

Sainte Suzanne

Compatible computation

time cost!

N

Overtopping Volume

Time series of

cumulative water

volume induced by

wave overtopping

Significant Wave Height Hs Cyclone

Overtopping

Offshore conditions


Very high computation time

cost (>severalhours)!

Wave overtopping modeling at local scale

> 8



Wave overtopping modeling at local scale

> 9



N

Volume cumulé de franchissement

Database of pre-

calculated

simulations for

~500 synthetic

cyclones

Cyclone

Overtopping

Offshore conditions


Very high computation

time cost!

• Take advantage of the database (~500 synthetic cyclones)

• Construct the link (statistical) betw.:

– The offshore conditions (maximum values for wave, sea level)

– The consequences induced by the cyclone:

• Overtopping occurence (0/1)

• Max of cumulative volume

Saint-Denis octobre 2017

Methods

• Take advantage of the database (~500 synthetic cyclones)

• Construct the link (statistical) betw.:

– The offshore conditions (maximum values for wave, sea level)

– The consequences induced by the cyclone:

• Overtopping occurence (0/1)

• Max of cumulative volume

• Use this link to predict with a negligible coputation time cost (<min)

• Tools

– A series of random forest approaches

– Flexible to any problem (classification, regression, etc.)


Methods

> 13

Decision

Tree

Decision

Tree Decision

Tree

Decision

Tree

Random Forest = ensemble of

randomized decision trees

Random Forest

> 14

Offshore

conditions leading

to flooding?

[Breiman (1984)]

Decision treeHs

<4.7m >4.7m

Tp

<14.15s >14.15s

NO FLOOD

Tp

<10.36s >10.36sHs

<5.9m >5.9m

FLOODFLOODNO

> 15

Offshore

conditions leading

to flooding?

[Breiman (1984)]

Decision treeHs

<4.7m >4.7m

Tp

<14.15s >14.15s

NO FLOOD

Tp

<10.36s >10.36sHs

<5.9m >5.9m

FLOODFLOODNO

> 16

Offshore

conditions leading

to flooding?

[Breiman (1984)]

Decision treeHs

<4.7m >4.7m

Tp

<14.15s >14.15s

NO FLOOD

Tp

<10.36s >10.36sHs

<5.9m >5.9m

FLOODFLOODNO

> 17

Random Forest

• Less sensitive to threshold values

• High accuracy

• Only a few parametersto tune

• Versatile to differentproblems(classification, regression, multi-output)

• Historical cases

– Dina-2002 et Dumile-2012;

• Use of the database (cross-validation)

• Performance criteria

• Accuracy

• True alarms

• False alarms


Validation?

Accuracy Predict true

alarms

Avoid

false

alarms

Occurrence of flooding - cross-validation

Cyclone

Overtopping

Dumile

Dina

Probability of flooding

Dina: [98-100%]; Dumile [90-100%]

Validation with historical events

Cyclone

Overtopping

TRUE

VOLUME

(m3)

Magnitude of flooding - cross-validation

Q2Cyclone

Overtopping

Dumile

Dina

Volume max

(m3)

Truth

Best estimate

95% Confidence

interval


Cyclone

Overtopping

Dumile

Dina

Volume max

(m3)

Truth

Best estimate

95% Confidence

interval


Cyclone

Overtopping

Large confidence interval widthindicator of RF error

> 24

Time-to-Event=the difference between the time instant when Volume>0 and the one when the considered cyclone is at a distance <400km from Reunion Island

Towards time evolution prediction

> 25

Adaptation of random-forest model to handle multivariate outputs

(Ishwaran et al. 2017)

Dina cyclone

Dumilecyclone



True

> 26

Adaptation of random-forest model to handle multivariate outputs

(Ishwaran et al. 2017)

Dina cyclone

Dumilecyclone



TrueTrue

• Method– Through the statistical analysis of precalculated numerical simulations

– A suite of Random forest procedures

– Flexible approach

• To overcome– Hydrodynamic simulator with high computation time cost

– The input-output relationship is non-smooth (highly nonlinear)

• Further work– Inputs/outputs are spatio-temporal quantities

– Integrate approximation uncertainties> 27

Speeding up EWS?

Early-warning system for cyclone-induced wave overtopping:

a suite of random forest approaches

Thank you for your

attention!

J. Rohmer1*, S. Lecacheux1, R. Pedreros1, D. Idier1, F. Bonnardot2

[email protected]

1: BRGM

2: Direction Régionale de Météo-France pour l’Océan Indien

mailto:[email protected]

Weather Forecast

Wind model

Flooding model

Metamodel

Wave model

Cyclone

Inundation

Overtopping

Sea conditions

Wind

Cascade of

uncertainties

This

presentation

Only one part of the problem…

> 30

Appendices

Wavewatch 3 two-way nested grids (10km => 300m)

Wave modeling at regional scale

Computing time ~ 25min on 24 CPU for 24h simulated

BEJISA le 02/01/2014 à 12UTC

Houlographe NortechMed RN4

> 31

Cum. volume

max

Lin.

correlation

Highly nonlinear

behaviour

Empirical analysis of the database


Use knowledge on Hs, Tp et TWL to predict the

occurrence of overtopping via regression

(random forest)

Empirical analysis of the database


PRINCIPES

10 Scénarios de

simulations


10 Scénarios de

simulations

Simulation

numérique

Etape couteuse en temps de calcul!

PRINCIPES


10 Scénarios de

simulations

Simulation

numérique10 Résultats

Aire d’inondation

PRINCIPES


Un scénario

Un résultat

Aire d’inondation

10 Scénarios de

simulations

Simulation


PRINCIPES


Un scénario

Aire d’inondation

Un résultat

10 Scénarios de

simulations

Simulation


PRINCIPES


Que dire là où n’a pas

fait de simulation ?

SANS utiliser le

simulateur couteux en

temps de calcul!!

?

?

?

?

Aire d’inondation

10 Scénarios de

simulations

Simulation


PRINCIPES


Combler les « trous »

avec un méta-modèle

(modèle statistique)

Aire d’inondation

10 Scénarios de

simulations

Simulation


PRINCIPES

> 42

Classification:

1. Splitting rule: maximize the decrease in

heterogeneity (measured by Gini impurity measure)

2. Stopping rule (Gini index does not evolve or max

number)

Class 1

Class 0

Classification using decision tree

> 43

N

p

A

A

A

ApApAN

ANApAp

AN

ANApApG

k

R

L

RRR

LLL )().(

)(

)()().(

)(

)()().( 010101

Inital domain

Left domain after splitting

Right domain after splitting

Probability of class k = {0;1}

Number of elements

[Breiman (1984)]

Gini impurity

measure before

splitting

AL

AR


> 44

AL

AR

AL AR

N

p

A

A

A

ApApAN

ANApAp

AN

ANApApG

k

R

L

RRR

LLL )().(

)(

)()().(

)(

)()().( 010101

Inital domain

Left domain after splitting

Right domain after splitting

Probability of class k = {0;1}

Number of elements

[Breiman (1984)]

G


Gini impurity

measure before

splitting

> 45

AL

AR

AL AR

AL AR

AL AR

GG

G


> 46Package R: tree; Approch of Malley (2012) for estimating the class probability

Probability of

belonging to class

1


> 47

Class 1

Class 1

Class 0

‘sure’

Class 0

Class 0 ‘almost sure’

Class 1

‘sure’

Class 1 ‘almost sure’

Class 1

‘medium

confidence’ Class 0

‘medium

confidence

Package R: tree; Approch of Malley (2012) for estimating the class probability


> 48

[Breiman (2001)]

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[Breiman (2001)]

> 50

[Breiman (2001)]

+ randomly select mtry

variables at each node

> 51

[Breiman (2001)]



treeii

iC

j

j njyyIErrCj

,...,1)ˆ(1

DD

> 52

[Breiman (2001)]; package R ranger



> 53

Probability

threshold to decide

class 1 or 0

[Metz (1978)]; package R pROC

> 54

Area under

the Roc

Curve AUC

[Metz (1978)]; package R pROC

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