This talk demonstrates the capability of particle filters to combine measurements to model simulation in a stochastic framework, in order to formulate some feedback information on the wildfire behavior. This is illustrated based on a reduced-scale controlled grassland fire experiment. Sampling Importance Re-sampling (SIR) and Auxiliary Sampling Importance Re-sampling (ASIR) filters were built on top of a level-set based front-tracking simulator in order to assimilate the time-evolving positions of the fire front and thereby correct the input environmental parameters of the fire spread model (i.e. vegetation properties, surface wind conditions). Reference published in October 2014 ➞ da Silva, W.B., Rochoux, M.C., Orlande, H., Colaço, M., Fudym, O., El Hafi, M., Cuenot, B., and Ricci, S. (2014) Application of particle filters to regional-scale wildfire spread, High Temperatures-High Pressures, International Journal of Thermophysical Properties Research, 43, 415-440.

1. Applications of particle filters in moving frontier problems:
Wildfire spread forecasting
W. Da Silva, M. Rochoux, H. Orlande, M. Colaço,
O. Fudym, M. El Hafi, B. Cuenot & S. Ricci
©
Pauline
Crombe/e
©
Domingo
Viegas

2. 2
INTRODUCTION
Wildfire
modeling
challenges
2
Uncertain)es
in
large-­‐scale
fire
spread
predic)ons
due
to
➔
large
range
of
length
scales
(pyrolysis
vegetaFon
scales
to
plume
dynamic
scales)
➔
unknown
boundary
and
iniFal
condiFons
• non-­‐homogeneous
and
poorly
defined
vegetal
fuels
• atmospheric
external
forcing
➔
difficult
validaFon
(lab-­‐scale
and
field-­‐scale
experiments)
cm
m
km
• Cost-­‐effecFve
• Front-­‐tracking
simulator
• Empirical
model
of
the
fire
front
spread-­‐rate
OperaFonally-­‐oriented
front-­‐tracking
simulator
©
ANR-­‐IDEA

3. 3
INTRODUCTION
Regional-­‐scale
wildfire
spread
modeling
3
➔
ParameterizaFon
of
the
rate
of
spread
(ROS)
as
a
funcFon
of
the
local
condiFons:
Weather
• Wind
velocity
and
direcFon
• Air
temperature
and
humidity
• Rainfall
Terrain
• Terrain
slope
Vegetal
fuel
• Moisture
content
• Depth
of
the
vegetal
layer
• Packing
raFo
• Fuel
parFcles
(density,
size,
…)
Front
topology
©
Cheney
(CSIRO)
➔
ISSUE
-­‐
Need
to
quanFfy
and
reduce
uncertainFes
in
• Model
formulaFon
• Input
model
parameters
• External
forcing
R
R(x, y, t) = f(uw, αsl, Mf , δf , βf , Σf ...)
FOCUS
©
ANR-­‐IDEA

4. INTRODUCTION
Why
parFcle
filters
for
tracking
wildfire
spread?
4
➔
In
principle,
parFcle
filters
can
handle
the
non-­‐lineariFes
present
in
a
physical
system
(in
a
more
formal
way
than
the
Kalman
filter
and
its
extensions).
• Time-­‐varying
wind
• Highly
heterogeneous
vegetal
fuel
properFes
that
change
over
Fme
Normalizing
constant
©
M.
Finney
(2011)
Skewed
fire
size
distribuFon

5. 5
OUTLINE
Wildfire
spread
forecasFng
using
parFcle
filters
5
©
Horus
(SDIS
66)
①
Regional-­‐scale
wildfire
spread
simulaFon
capability
②
ParFcle
filter
algorithms
③
ApplicaFon
to
a
controlled
burning
experiment

6. Focus:
surface
fire
spread
➔
Build
a
simplified
model
that
gives
the
Fme-­‐evoluFon
of
the
flame
front
locaFon
• Front-­‐tracking
strategy
• 2-­‐D
propagaFon
within
the
vegetal
fuel
bed
(li/er)
PART.
1
PART.
2
PART.
3
InformaFon
at
regional-­‐scales:
model
6
➔
Level-­‐set-­‐based
front
propagaFon
solver
• 2-­‐D
variable:
reacFon
progress
variable
c
• Flame
front
marker:
isoline
c
=
0.5
∂c
∂t
= R|∇c|
FIREFLY:
c
=
1
c
=
0
➔
Issue:
How
to
accurately
describe
uncertainFes
in
input
parameters
of
the
rate
of
spread
R?

7. PART.
1
PART.
2
PART.
3
InformaFon
at
regional-­‐scales:
data
7
➔
GeolocaFon
of
acFve
fire
areas
• Middle
InfraRed
(MIR)
camera
aboard
• FRP
(Fire
RadiaFve
Power)
measurements
sensiFve
to
acFve
fire
areas
Airborne-­‐based
thermal
infrared
imaging
➔
Requirements
for
inverse
problems
• High-­‐spaFal
resoluFon
imagery
(<
30
m)
• Short
revisit
period
X (m)
Y(m)
0 0.5 1 1.5 2 2.5 3 3.5 4
0
0.5
1
1.5
2
2.5
3
3.5
4
©
Ronan
Paugam
(King’s
College)
Assume
iso-­‐
temperature
for
fire
igniFon
(600K)
Temperature
field
[K]
ReconstrucFon
of
fire
front
posiFon
©
D.
Viegas

8. PART.
1
PART.
2
PART.
3
Inverse
problem
strategy
8
Why?
1-­‐
Uncertainty
on
inputs
Uncertainty
on
outputs
2-­‐
Find
best
esFmate
of
control
variables
given
available
observaFons
➔
Which
input
model
parameters
are
criFcal
to
control?
• SensiFvity
analysis
of
Rothermel
spread-­‐rate
model
• IllustraFon
of
the
non-­‐lineariFes
present
in
the
wildfire
spread
model
R(x, y, t) = f(uw, Mf , δf , βf , Σf , ...)
Mf
[!]
![m/s]
0 0.05 0.1 0.15 0.2 0.25 0.3
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
R [m/s]
Mf [-]
Wind-­‐aided
fire
spread
(1
m/s)
Short
grass
Long
grass
Timber
li/er
Control
parameters
Simulated
fronts
Firefly
simulator
¤ level-­‐set
simulator
¤
moisture
content
Mf
¤
fuel
parFcle
surface/volume
Σf
¤
wind
speed
uw

9. PART.
1
PART.
2
PART.
3
Inverse
problem
strategy
9
Why?
1-­‐
Uncertainty
on
inputs
Uncertainty
on
outputs
2-­‐
Find
best
esFmate
of
control
variables
given
available
observaFons.
➔
How
to
compare
simulated
fire
front
posiFons
and
observaFons?
Discrete
Fme-­‐evolving
fire
front
posiFons
Uncertainty
range
for
each
front
posiFon
x
y
Fme
Control
parameters
Simulated
fronts
Firefly
simulator
¤ level-­‐set
simulator
¤
moisture
content
Mf
¤
fuel
parFcle
surface/volume
Σf
¤
wind
speed
uw
ObservaFons
prior
distribuFon
likelihood
DistribuFons
for
modeling
and
observaFon
errors
¤ selecFon
of
the
front
at
the
assimilaFon
Fme
xk zk
hkObserva)on
model

10. PART.
1
PART.
2
PART.
3
Inverse
problem
strategy
10
Why?
1-­‐
Uncertainty
on
inputs
Uncertainty
on
outputs
2-­‐
Find
best
esFmate
of
control
variables
given
available
observaFons.
Control
parameters
Simulated
fronts
Firefly
simulator
¤ level-­‐set
simulator
¤
moisture
content
Mf
¤
fuel
parFcle
surface/volume
Σf
¤
wind
speed
uw
ObservaFons
prior
distribuFon
Bayesian
filtering
Data-­‐driven
feedback
Simulated
front
Observed
front
(xf , yf )1
(xf , yf )p
(xf , yf )j
(xo
f , yo
f )j
(xo
f , yo
f )1
(xo
f , yo
f )p
Posterior
distance
Extended
state
es)ma)on

11. PART.
1
PART.
2
PART.
3
Inverse
problem
strategy
11
➔
Bayesian
filtering
in
2
steps:
• PredicFon
of
the
physical
model
• Update
of
the
control
parameters
based
on
Bayes’
theorem
πposterior(xk) = π(xk|zk) =
πprior(xk)π(zk|xk)
π(zk)
Likelihood
(measurement
model
including
uncertainFes)
Normalizing
constant
πprior(xk) = π(xk|xk−1)
➔
ISSUE:
How
to
describe
the
prior
model?
• Is
represented
as
a
transiFon
probability
density
from
Fme
(k-­‐1)
to
Fme
k
• Includes
a
random
walk
model
for
the
parameter
evoluFon
➔
SOLUTION:
ParFcle
filters
to
obtain
the
posterior
• Monte-­‐Carlo
technique:
representaFon
of
the
posterior
by
a
set
of
random
samples
(parFcles)
with
associated
weights

12. reality
model
predicFon
diagnosis
measurements
analysis
PART.
1
PART.
2
PART.
3
Inverse
problem
strategy
12
➔
Bayesian
filtering
in
2
steps:
• PredicFon
of
the
physical
model
• Update
of
the
control
parameters
based
on
Bayes’
theorem
πposterior(xk) = π(xk|zk) =
πprior(xk)π(zk|xk)
π(zk)
Likelihood
(measurement
model
including
uncertainFes)
predicFon
update
predicFon
➔
SequenFal
esFmaFon
Normalizing
constant

13. PART.
1
PART.
2
PART.
3
Inverse
problem
strategy
13
➔
Sampling
Importance
Resampling
(SIR)
algorithm
1
i
N
parFcles
• Ref.
RisFc
et
al.
(2004),
Beyond
the
Kalman
filter
1)
PredicFon
π(xk|xi
k−1)
2)
Likelihood
4)
Resampling
(avoid
parFcles
with
negligible
weight)
3)
Update
π(xk|zk)(xi
k, wi
k)
(xi∗
k , 1/N)
• LimitaFon
in
the
parallelizaFon
• Loss
of
diversity
(sample
impoverishment)
ISSUES
wi
k = π(zk|xi
k)

14. PART.
1
PART.
2
PART.
3
Inverse
problem
strategy
14
➔
New
algorithm:
Auxiliary
Sampling
Importance
Resampling
(ASIR)
1
i
N
parFcles
• Ref.
W.
Da
Silva
et
al.,
ApplicaFon
to
one-­‐dimensional
solidificaFon
problem,
COBEM
2011
• Key
idea:
improve
the
prior
informaFon
based
on
some
point
esFmate
μi
k
using
an
auxiliary
set
of
parFcles
1)
PredicFon
π(xk|xi
k−1)
2)
Likelihood
4)
Resampling
(avoid
parFcles
with
negligible
weight)
3)
Update
π(xk|zk)(xi
k, wi
k)
wi
k = π(zk|µi
k) wi
k−1
wi
k = π(zk|xi
k)
(xi∗
k , wi∗
k )
• more
realisFc
parFcles
• less
sensiFve
to
outliers
than
SIR
ADDED-­‐VALUES
FOR
ASIR

15. 15
PART.
1
PART.
2
PART.
3
ApplicaFon
to
controlled
burning
experiment
15
Environmental
condi)ons
➔
Reduced-­‐scale
fire:
4m
x
4m
➔
Homogeneous
short
grass
vegetaFon
• Fuel
bed
depth:
8
cm
• Moisture
content:
22%
➔
Mean
rate
of
spread:
1-­‐2
cm/s
(max.
5
cm/s)
➔
ObservaFon:
• Error
due
to
the
resoluFon
of
the
MIR
camera
• Error
esFmaFon:
5
cm
(1%
burning
area)
2min14s
3min10s
2min42s
1min28s
1min46s
!
Mean
wind
1
m/s,
307°
Time
series
of
surface
temperature
field
(Ronan
Paugam,
King’s
College
of
London)
Time

16. 16
PART.
1
PART.
2
PART.
3
ApplicaFon
to
controlled
burning
experiment
16
3
control
parameters
➔
Wind
magnitude
(fluctuaFons
between
0-­‐2
m/s)
➔
Fuel
moisture
content
(22%)
➔
Fuel
parFcle
surface/volume
(11500
m-­‐1)
2min14s
3min10s
2min42s
1min28s
1min46s
!
Mean
wind
1
m/s,
307°
Time
series
of
surface
temperature
field
(Ronan
Paugam,
King’s
College
of
London)
Time
R(x, y, t) = f(uw, Mf , δf , βf , Σf , ...)

17. PART.
1
PART.
2
PART.
3
ApplicaFon
to
controlled
burning
experiment
17
➔
Sequen)al
es)ma)on:
5
successive
esFmaFons
of
the
control
parameters
SIR
algorithm
(N
=
200)
ASIR
algorithm
(N
=
50)
Results:
• Consistent
results
of
the
SIR
and
ASIR
algorithms
• Good
tracking
of
the
observed
fire
front.

18. PART.
1
PART.
2
PART.
3
ApplicaFon
to
controlled
burning
experiment
18
➔
Sequen)al
es)ma)on:
5
successive
esFmaFons
of
the
control
parameters
SIR
algorithm
(N
=
200)
ASIR
algorithm
(N
=
50)
Moisture
content
Fuel
parFcle
surface/
volume
99%
Confidence
interval
Mean
value
EKF
result

19. PART.
1
PART.
2
PART.
3
ApplicaFon
to
controlled
burning
experiment
19
➔
Sequen)al
es)ma)on:
5
successive
esFmaFons
of
the
control
parameters
Wind
magnitude
(m/s)
SIR
algorithm
(N
=
200)
ASIR
algorithm
(N
=
50)
Results:
• Same
level
accuracy
reached
by
the
SIR
and
ASIR
algorithms
• ValidaFon
against
independent
measurements
of
the
wind
velocity
magnitude,
even
though
the
wind
is
subject
to
significant
fluctuaFons
In-­‐situ
measurements
of
the
wind
magnitude
In-­‐situ
measurements
of
the
wind
magnitude

20. CONCLUSIONS
ApplicaFons
of
parFcle
filters
to
moving
fronFer
problems
•
SIR
and
ASIR
par)cle
filters
able
to
➔
achieve
mulF-­‐parameter
esFmaFon
➔
reduce
fire
modeling
uncertainFes
➔
track
fire
front
for
a
controlled
burning
experiment
•
Valida)on
of
the
ASIR
algorithm:
shown
to
be
less
computaFonally
expensive
than
the
SIR
algorithm
in
a
wide
range
of
experiments
[W.
Da
Silva
et
al.,
ApplicaFon
to
one-­‐dimensional
solidificaFon
problem,
COBEM
2011]

21.
•
Comparison
to
Ensemble
Kalman
filter
algorithm
(CERFACS-­‐University
of
Maryland,
M.
Rochoux’s
PhD
thesis)
•
Applica)ons
of
ASIR
par)cle
filters
to
new
fields
of
applica)ons
(Wellington)
➔
temperature
field
predicFon
of
a
mulF-­‐layer
composite
pipeline
➔
reservoir
history
matching
problem
PERSPECTIVES
ApplicaFons
of
parFcle
filters
to
moving
fronFer
problems
Parameter
esFmaFon
• CorrecFon
on
the
model
physics
(dynamic
learning)
• Surrogate
model
of
the
fire
spread
simulator
to
limit
computaFonal
cost
[Rochoux
et
al.
(2012),
CTR
Summer
Program]
Polynomial
Chaos

22. Thank
you
for
your
a/enFon!

23. Acknowledgments
•
FAPERJ,
CAPES
and
CNPq,
Brazilian
agencies
and
French
Ministry
of
foreign
affairs.
•
Centre
NaFonal
pour
la
Recherche
ScienFfique
(CNRS).
•
Project
«11STIC06-­‐I3PE-­‐Inverse
Problems
in
Physical
Property
EsFmaFon».
•
Project
«IDEA
ANR-­‐09-­‐COSI-­‐006-­‐06,
Wilfires:
From
PropagaFon
to
Atmospheric
Emissions»
•
Dept.
of
Geography,
King’s
College
of
London
(MarFn
Wooster
and
Ronan
Paugam
for
the
data
of
the
controlled
burning
experiment).