6/27/2014 Slide 1

Sensor-Driven Modeling

to Reduce Uncertainties

in Simulations of Wildland Fire Spread

Mélanie Rochoux1,2,3,

Sophie Ricci1,2, Bénédicte Cuenot1, Arnaud Trouvé4 1CERFACS, Toulouse (France)

2SUC-URA1875, CNRS (France)

3Ecole Centrale Paris (France)

4University of Maryland (USA)

6/27/2014 Slide 2

Problem Statement

Current fire modeling capabilities are far from being

predictive

• Modeling challenge: large uncertainties in

physical/numerical modeling of complex multi-physics

phenomena

Compartment/wildland fires: turbulence; combustion; soot; thermal

radiation; convective heat transfer; fire suppression systems; solid

fuel sources; geometrical changes

• Data challenge: large uncertainties in input parameters used

in fire models

Compartment fires: solid fuel sources; wall properties

Wildland fires: vegetation properties; topographical conditions;

meteorological conditions

6/27/2014 Slide 3

Problem Statement

Develop predictive fire modeling capabilities

• Data assimilation: reduce fire modeling uncertainties by

integrating fire modeling and fire sensing technologies

Take advantage of progress made in sensor technology and ubiquity

of sensor networks

• A well-established approach in many areas of science (e.g.,

weather and climate modeling applications)

• Application to: detection of incipient fires; post-event

forensic investigations; real-time emergency response

management

6/27/2014 Slide 4

Theoretical Framework

Data assimilation • Find best estimate of the system state/parameters (fire front position,

ROS model parameters) at present/future times given observations (i.e.,

fire front position) made at earlier times

Observations

System state

Model parameters Model outputs Forward model

Inverse model

Control variables

y f = H(x f )

x f

yo

xa = x f + K(yo - H(x f ))

(forecast)

(analysis)

6/27/2014 Slide 5

Theoretical Framework

Data assimilation

• Inverse model

• Solution of inverse problem using a variational approach

(optimization/control theory) or a statistical Bayesian

approach (probability theory)

Optimization theory: minimize a cost function

Accounts explicitly for both modeling and observation errors

modeling errors observation errors

J(x) =1

2(x- x f )T B-1(x- x f )+

1

2(yo - H (x))T R-1(yo - H(x))

6/27/2014 Slide 6

Theoretical Framework

K = Cxy

(Cyy

+Cyoyo )-1

xa = x f + K(yo - H(x f ))

Data assimilation

• Ensemble Kalman Filter (EnKF) algorithm

Calculation of the gain matrix K based on an ensemble of simulations

of the forward model, yk = H(xf,k), and a statistical evaluation of the

covariance matrices Cxy and Cyy

6/27/2014 Slide 7

Sensor-driven simulations of wildfire spread

• Regional-scale modeling ( 10 m < L < 10 km)

Surface fires ( crown fires, ground fires, firebrands)

Front topology

Local propagation speed of the front called the rate of spread (ROS)

Burnt vegetation

Unburnt vegetation

Front

Rate of spread ROS

Data-Driven Fire Modeling

6/27/2014 Slide 8

Sensor-driven simulations of wildfire spread

• Forward model

Model description of the rate of spread (Rothermel)

ROS = f ([df, ¢¢m

f,r

f,S

f,M

f],N

slope,u

wind)

Data-Driven Fire Modeling

6/27/2014 Slide 9

Sensor-driven simulations of wildfire spread

• Forward model

Level-set-based solver for the fire front propagation equation (cheap)

(Rehm & McDermott 2009)

RK2

TVD scheme with Superbee

slope limiter

Data-Driven Fire Modeling

¶c

¶t= ROS |Ñc |

c = 1

c = 0

6/27/2014 Slide 10

Sensor-driven simulations of wildfire spread

• Assume real-time fire front observations

Data-Driven Fire Modeling

Airborne Spaceborne

Requirements for data assimilation

•High-spatial resolution images (10 m)

•High-temporal resolution (10 minutes)

6/27/2014 Slide 11

Data assimilation • Find best estimate of the system state/parameters (fire front position,

ROS model parameters) at present/future times given observations (i.e.,

fire front position) made at earlier times

Observed front

Fire front position

ROS parameters Simulated front Forward model

Inverse model

Control variables

y f = H(x f )

x f

yo

Data-Driven Fire Modeling

EnKF

FIREFLY simulator

moisture content Mf

fuel particle surface/volume Σf

wind speed and direction uw

6/27/2014 Slide 12

Verification tests (xtrue exists) (control variables: fire front position)

• Spatially-uniform test with constant ROS but uncertain ignition location,

t = 200 s

Data-Driven Fire Modeling

60 70 80 90 100 110 120 130 14060

70

80

90

100

110

120

130

140

x (m)

y (

m)

60 70 80 90 100 110 120 130 14060

70

80

90

100

110

120

130

140

x (m)

y (

m)

true

forecast

observation true observation

analysis

6/27/2014 Slide 13

Verification tests (control variables: fire front position; SE algorithm)

• Spatially-uniform test with constant ROS but uncertain ignition location,

t = 200 s

Data-Driven Fire Modeling

d(true,forecast)

d(true,analysis)

s f

s a

(so = observation error)

6/27/2014 Slide 14 320 330 340 350 360 370 380330

340

350

360

370

380

x (m)

y (

m)

Verification tests (control variables: fire front position; SE algorithm)

• Spatially-varying test with uncertain ROS model parameters and

uncertain ignition location, t = 400 s

Data-Driven Fire Modeling

true observation

analysis

300 340 380 420280

320

360

400

440

480

520

x (m)

y (

m)

forecast

true

6/27/2014 Slide 15 260 280 300 320 340 360 380 400 420300

320

340

360

380

400

420

440

x(m)

y(m

)

Verification tests (control variables: fire front position; SE algorithm)

• Spatially-varying test with uncertain ROS model parameters, multiple

analysis cycles, t2 = 300 s and t4 = 600 s

Data-Driven Fire Modeling

true observation

mean analysis

mean forecast

6/27/2014 Slide 16

Validation test • Controlled grassland fire (flat and horizontal, open field) (Paugam,

King's College London)

• Domain: 4 ´ 4 m2; vegetation: homogeneous grass layer (8 cm thickness) 8 cm; moisture content: 22%; wind conditions: 1 m/s; mean direction: 307° (N = 0°); mean ROS: 1-2 cm/s (max. 5 cm/s); observation error: 5 cm (1% burning area)

Data-Driven Fire Modeling

t = 78s t = 50s t = 106s

Data, Ronan Paugam http://wildfire.geog.kcl.ac.uk/index.php/ronan

Time

6/27/2014 Slide 17

Validation test • Controlled grassland fire (Paugam, King's College London)

• Data processing: extraction of flame contour from temperature images

Data-Driven Fire Modeling

6/27/2014 Slide 18

Validation test (control variables: ROS parameters (Mf,Sf,uw,x,uw,y) in

PE-based algorithm; fire front position in SE-based algorithm)

• Controlled grassland fire (Paugam, King's College London); t = 64 s

Data-Driven Fire Modeling

+ observations

- mean free forecast: SE-based (solid line); PE-based (dashed line)

- mean analysis: SE-based (solid line); PE-based (dashed line)

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

1.5

2

x [m]

y [

m]

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

1.5

2

x [m]

y [

m]

mean analysis mean free forecast

(no DA)

6/27/2014 Slide 19

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

1.5

2

x [m]

y [

m]

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

1.5

2

x [m]

y [

m]

Validation test (control variables: ROS parameters (Mf,Sf,uw,x,uw,y) in

PE-based algorithm; fire front position in SE-based algorithm)

• Controlled grassland fire (Paugam, King's College London); t = 92 s

(left) and t = 106 s (right)

Data-Driven Fire Modeling

+ observations

- mean analysis: SE-based (solid line); PE-based (dashed line)

mean analysis mean analysis

6/27/2014 Slide 20

Validation test (control variables: ROS parameters (Mf,Sf,uw,x,uw,y) in

PE-based algorithm; fire front position in SE-based algorithm)

• Controlled grassland fire (Paugam, King's College London); t = 106 s

(with data assimilation and with an update at t = 92 s)

Data-Driven Fire Modeling

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.5

1

1.5

2

x [m]

y [

m]

+ observations

- mean forecast: SE-based (solid line); PE-based (dashed line)

mean forecast

6/27/2014 Slide 21

Conclusion

Sensor-driven fire modeling

• A promising novel approach:

Reduce fire modeling uncertainties by integrating fire modeling and

fire sensing technologies

Take advantage in progress made in sensor technology and ubiquity

of sensor networks

• EnKF-FIREFLY

Capable of correcting inaccurate predictions of the fire front position

and of providing an optimized forecast of the wildfire behavior

Parameter estimation approach: correction of the ROS model (mid-

and long-term forecast)

State estimation approach: correction of the fire front location (short-

term forecast)

6/27/2014 Slide 22

Conclusion

Sensor-driven fire modeling

• Future work (EnKF-FIREFLY)

Dual state estimation/parameter estimation approach

Treat configurations with complex topography

Integration of EnKF-FIREFLY into a CFD atmospheric model (e.g.,

Weather Research and Forecasting Model - WRF) to describe the

interactions between the fire and the atmosphere

Include treatment of fire plume

Modify ROS model in order to: (1) improve Rothermel’s model; (2)

include non-local effects

6/27/2014 Slide 23

Complex Topography

Extension of EnKF-FIREFLY to cases with complex terrain

(Lautenberger 2013)

(Emery 2013)

• gs: slope angle

• ga: aspect angle

Nslope

sin(gs)sin(g

a)

sin(gs)cos(g

a)

cos(gs)

Horizontal plane

North

y

x East

Vertical direction

z

a

s

6/27/2014 Slide 24

020

4060

80100

120140

160180

200 020

4060

80100

120140

160180

2000

10203040

y (m)x (m)

Complex Topography

Extension of EnKF-FIREFLY to cases with complex terrain

(Emery 2013)

• ROS calculated in projected horizontal plane:

ROS* =ROS

1+ tan2(gs)cos2(q -g

a)

wind