This talk presents the preliminary prototype data-driven wildfire spread simulator based on the extended Kalman filter (EKF) with a parameter estimation approach. Since then, FireFly was extended to an ensemble Kalman filter (EnKF) to better account for model nonlinearities. Reference published in January 2013 ➞ Rochoux, M.C., Delmotte, B., Cuenot, B., Ricci, S., and Trouvé, A. (2013) Regional-scale simulations of wildland fire spread informed by real-time flame front observations, Proceedings of the Combustion Institute, 34, 2641-2647, doi: 10.1016/j.proci.2012.06.090

1. Regional-­‐scale
simula/on
of
wildfire
spread
informed
by
real-­‐/me
flame
front
observa/ons
M.
Rochoux
B.
DelmoAe
B.
Cuenot
S.
Ricci
A.
Trouvé
Wild
and
Soo/ng
Fires
–
Ref.
2C10
34th
Interna/onal
Symposium
on
Combus/on

2. Spain:
12,000
ha
burned
Colorado:
80,000
ha
burned
Need
for
a
predic/ve
simulator
of
fire
spread

3. 3
“Regional-­‐scale
simula/on
of
wildfire
spread”
Observa*on:
Wildfires
feature
a
front-­‐like
geometry
at
regional
scales
•
scales
ranging
from
meters
up
to
several
kilometers
•
thin
flame
zone
propaga/ng
normal
to
itself
towards
unburnt
vegeta/on
•
local
propaga/on
speed
of
the
front
called
the
rate
of
spread
Г
Burnt
vegeta*on
Unburnt
vegeta*on
Front
Issue:
How
to
accurately
describe
the
rate
of
spread
Г?
Introduc/on
Rate
of
spread
Γ

4. 4
Burnt
vegeta*on
Unburnt
vegeta*on
Front
Introduc/on
Rate
of
spread
Γ
•
Sub-­‐model
for
the
local
rate
of
spread
Г
(m/s)
•
Level-­‐set-­‐based
front
propaga/on
simulator
“Regional-­‐scale
simula/on
of
wildfire
spread”
[Ref.
Rothermel
(1972),
Technical
report,
US
Department
of
Agriculture,
Forest
Service]
Γ(x, y) = P
uw(x, y), Mf , Σ, δ
§
magnitude
§
direc/on
§
moisture
content
Mf
§
par/cle
surface/volume
Σ
§
layer
ver/cal
thickness
δ
Wind
Vegeta*on
(fuel)
Semi-­‐empirical
Rothermel
model
Issue:
How
to
properly
describe
vegeta*on
and
wind
parameters?

5.
↘
Aboard
a
surveillance
aircrae
↘
Assume
threshold
temperature
for
fire
igni/on
(600K)
5
“Real-­‐/me
flame
front
observa/ons”
Data
analysis
Fire
event
detec*on
Data
acquisi*on
Infrared
camera
at
medium
wavelengths
(no
gas
emission)
Reconstruc/on
of
fire
front
loca/ons
Important:
Accoun*ng
for
measurement
error
5
Introduc/on

6. 6
Simula/ons
“informed
by”
measurements
Introduc/on
Why?
1
-­‐
Uncertainty
on
inputs
Uncertainty
on
outputs
2-­‐
Find
best
es/mate
of
control
variables
at
/me
ti
given
observa/ons
for
tit
?
Data
Assimila*on
strategy
oil
reservoir
modeling
Resolu*on
of
an
inverse
problem
y
=
H(x)
Observa/ons
Boundary
condi/ons
Ini/al
condi/on
Model
parameters
Model
outputs
Forward
model
H
Data
assimila/on
algorithm
-­‐
Control
variables
OBJECTIVE:
Develop
a
data
assimila/on
strategy
for
flame
spread
applica/ons

7. tobs,1
tobs,2
error
Which
type
of
observa/ons?
Observa/ons
7
1 Data
assimila/on
algorithm
7
Quan*ty
of
interest:
discrete
/me-­‐evolving
flame
front
posi/ons
yo
R
=
Each
front
point
is
a
random
variable
defined
by
a
Gaussian
PDF
(mean,
variance).
Observa*on
error
covariance
matrix
Variance
of
one
front
point
Covariance
of
a
pair
of
front
points

8. Observa/ons
8
1 Data
assimila/on
algorithm
Control
variables
Model
outputs
Forward
model
H
8
① Model
parameters
§ Moisture
content
§ Fuel
surface/volume
ra/o
§ Wind
velocity
magnitude
② Model
uncertainty
Each
model
parameter
is
a
random
variable
defined
by
a
Gaussian
PDF.
-­‐
Model
propaga*on
-­‐
Selec*on
of
front
points
obs.
simula*ons
Comparable
simulated
quan/ty
mean
+
variance
Error
covariance
matrix
B
1
parameter
mul/-­‐parameter

9. Observa/ons
9
1 Data
assimila/on
algorithm
Control
variables
Model
outputs
Forward
model
H
9
① Model
parameters
§ Moisture
content
§ Fuel
surface/volume
ra/o
§ Wind
velocity
magnitude
② Model
uncertainty
Each
model
parameter
is
a
random
variable
defined
by
a
Gaussian
PDF.
-­‐
Model
propaga*on
-­‐
Selec*on
of
front
points
Distance
observa/on-­‐model
simula/on
-­‐
obs.
simula*on
distance

10. Observa/ons
10
1 Data
assimila/on
algorithm
Control
variables
Model
outputs
Forward
model
H
10
-­‐
Data
assimila/on
algorithm
Model
feedback
Model
feedback
Inverse
problem
How?
Maximize
Resolu*on
of
an
inverse
problem
y
=
H(x)
Pa
(x) = P(x = xt
| y = yo
)
Minimiza/on
of
a
cost
func/on
J(x) =
1
2
(x − xb
)T
B−1
(x − xb
) +
1
2
(yo
− H(x))T
R−1
(yo
− H(x))
model
error
observa*on
error
Gaussian
PDFs

11. itera*on
1
itera*on
2
itera*on
3
itera*on
4
11
1 Data
assimila/on
algorithm
11
Extended
Kalman
Filter
(EKF)
Formula*on
of
a
gain
matrix
Ki
•
assume
linear
rela/onship
between
control
parameters
and
model
outputs
For
each
data
assimila*on
cycle
i:
Model
error
Observa*on
error
Model
Jacobian
solu/on:
itera/ve
computa/on
of
the
gain
matrix
via
the
update
of
the
model
Jacobian
H
xa
i = xb
i + Ki
yo
− H(xb
i )
Ki = BiHT
i
HiBiHT
i + R
−1

12. 12
1 Data
assimila/on
algorithm
12
Extended
Kalman
Filter
(EKF)
Formula*on
of
a
gain
matrix
Ki
•
assume
linear
rela/onship
between
control
parameters
and
model
outputs
For
each
data
assimila*on
cycle
i:
Model
error
Observa*on
error
Model
Jacobian
xa
i = xb
i + Ki
yo
− H(xb
i )
Ki = BiHT
i
HiBiHT
i + R
−1
0 50 100 150 200 250 300 350 400
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
0.36
0.38
0.4
o
(m)
meanoftheanalysis(m.s
1
)
Relation between the mean of the analysis and the observations error with f
=0.05
Observation error (m)
Observa*on
KalmanFiltersolution(posterior)
Increasing
confidence
in
observa*ons
Prior
•
interpreta/on:
weighted
average,
with
more
weight
being
given
to
informa/on
with
higher
certainty.

13. Grassland
controlled
burning
Data
provided
by
Ronan
Paugam
hAp://wildfire.geog.kcl.ac.uk/index.php/ronan
↘
Domain
of
propaga/on:
4m
x
4m
↘
Homogeneous
short
grass
o
Height:
8cm
o
Moisture
content:
21.7%
↘
Wind
o
Mean
magnitude:
1.3m/s
o
Mean
direc/on:
307°
(N=
0°)
↘
Mean
rate
of
spread:
1.5
cm/s
↘
Fire
dura/on:
350s
Condi*ons
13
13
2 Applica/on
case
13
Infrared
camera
aboard
a
cherry
picker:
Wind
Time
(s)

14. Γ(x, y) = P
uw(x, y), Mf , Σ, δ
•
Es/ma/on
of
2
fuel
model
parameters
Control
parameters
Grassland
controlled
burning
Init.
condi/on
t
=
78s
Assimila/on
Forecast
Free
run
Op/mal
•
1
data
assimila/on
cycle
Grassland
controlled
burning
14
14
2 Applica/on
case
14
§
moisture
content
Mf
§
par/cle
surface/volume
Σ
t
=
50s
t
=
106s
observa/on
(assumed
constant
over
the
fire
dura*on)
Wind
(very
high
observa/on
confidence
match
the
observed
fronts)

15. •
2-­‐parameter
EKF
results:
Wind
• Uncertainty
modeling
o Observa/on
(camera
spa/al
resolu/on):
4.7cm
o Model:
30%
uncertainty.
Grassland
controlled
burning
Grassland
controlled
burning
15
15
2 Applica/on
case
15
Control
parameters
Prior
Solu*on
Moisture
content
(%)
21.7
11.0
Fuel
part.
S/V
(m-­‐1)
4921
13193
Ÿ observa/on
-­‐-­‐
free
run
-­‐-­‐
op/mal
X
(m)
Y
(m)
• Comments
o Reduc/on
of
uncertainty
on
simula/on.
o The
corrected
parameters
stay
within
a
physical
range.

16. •
4-­‐parameter
EKF
results:
Wind
Grassland
controlled
burning
Grassland
controlled
burning
16
16
2 Applica/on
case
16
Control
parameters
Prior
Solu*on
Moisture
content
(%)
21.7
7.1
Fuel
part.
S/V
(m-­‐1)
4921
7185
Wind
magnitude
(m/s)
1.3
0.38
Wind
direc/on
(°)
307
300
Ÿ observa/on
-­‐-­‐
free
run
-­‐-­‐
op/mal
(4p)
-­‐-­‐
op/mal
(2p)
X
(m)
Y
(m)
• Comments
o More
consistent
front
topology
with
respect
to
the
observa/ons.
o Dynamic
learning:
the
value
of
the
parameters
is
case-­‐
dependent.
Γ(x, y) = P
uw(x, y), Mf , Σ, δ

17. •
Predic/ve
capability:
improve
forecast
of
fire
spread
Grassland
controlled
burning
Grassland
controlled
burning
17
17
2 Applica/on
case
17
Init.
condi/on
t
=
78s
Assimila/on
Forecast
Op/mal
t
=
50s
t
=
106s
Observa/on
Y
(m)
X
(m)
X
(m)
Ÿ observa/on
-­‐-­‐
free
run
-­‐-­‐
op/mal
(4p)
-­‐-­‐
op/mal
(2p)
Y
(m)
Step.2
-­‐
Forecast
Step.1
-­‐
Correc/on

18. Data
assimila*on
for
flame
spread
propaga*on:
Proof
of
concept
•
Development
of
a
prototype
able
to
↘
Achieve
a
mul/-­‐parameter
es/ma/on.
↘
Track
fire
front
loca/ons
for
real
and
synthe/cal
observa/ons.
18
Conclusion
Ÿ observa/on
-­‐-­‐
free
run
-­‐-­‐
op/mal
(4p)
Ongoing
research
•
Ensemble-­‐based
approach
(Monte-­‐
Carlo
combined
to
data
assimila/on).
•
More
accurate
descrip/on
of
the
PDFs
of
the
model
inputs
and
outputs.

19.
Thank
you
for
your
a9en:on!
Rochoux
et
al.
(2012),
Proc.
Combust.
Inst.