Demonstrating the Validity of Wildfire DDDAS

The DDDAS Wildfire Team

Presented by Janice CoenNational Center of Atmospheric Research

ICCS’06May 2006

Supported by NSF under grants ACI-0325314, ACI-0324989, ACI-0324988, ACI-0324876, and ACI-0324910

The Wildfire DDDAS TeamUniversity of Colorado at Denver and Health Science CenterDepartment of Mathematical Sci.Jan Mandel (PI, Lead PI)Lynn Bennethum (Co-PI)Leo Franca (Co-PI)Craig Johns (prior Co-PI)Tolya Puhalskii (prior Co-PI)Mingeong Kim (graduate student)Vaibhav Kulkarni (graduate student)Jonathan Beezley (graduate student)

National Center for Atmospheric ResearchJanice Coen (PI)

Texas A&M UniversityDept. of Computer ScienceGuan Qin (PI)Wei Zhao (prior PI)Jianjia Wu (graduate student)

Rochester Institute of TechnologyCenter for Imaging ScienceAnthony Vodacek (PI)Robert Kremens (Co-PI)Ambrose Onoye (postdoc)Ying Li (graduate student)Zhen Wang (graduate student)Matthew Weinstock (undergrad. student)

University of KentuckyDept. of Computer ScienceCraig Douglas (PI)Deng Li (postdoc)Wei Li (graduate student)Adam Zornes (graduate student)

Other Collaborators:USDA Forest Service Missoula Tech. Development Center – UAVs, SAFE

Univ. of Montana (Natl. Cntr. Landscape Fire Analysis)Univ. of Utah - SCIRun enhancements

The ObjectiveA Dynamic Data Driven Application System (DDDAS) for short-range forecasts of wildfire behavior with models steered by real-time weather data, fire-mapping images, and sensor streams.

Goals

• The model– faster than real time– calibrated from measurements

• Data assimilation– sparse data (weather stations)– large image datasets (aerial photographs)– data acquisition steering– data arriving delayed and out of order– capable of adjusting a highly nonlinear model

• Real-time visualization over the internet in the field

Wildfire DDDAS Structure

Synthetic data

Map sources (GIS)

Fuel DataSensors, telemetry

Forecast

Weather

Fire

Model Observation function

Aerial imaging

Adjust Compare

Data Assimilation

Initial conditions

Weather data

Data Acquisition

Real data pool

Real time data

Interpret

Modular Software Structure: Major components are interchangeable

Model1. NCAR coupled weather-fire model2. Standalone PDE fire model (new)3. Improved PDE fire model, coupled with

weather (future) Data Assimilation1. Ensemble Kalman Filter, improved efficiency2. Predictor-Corrector nonlinear filter (new,

future)

The NCAR coupled weather-fire model

Environmental Factors that affect Wildland Fire Behavior

Fuel Moisture, mass/area, size, hardwood vs. conifer, spatial continuity, vertical arrangement

Weather wind, temperature, relative humidity, precipitation Weather CHANGES: fronts, downslopewinds, storm downdrafts, sea/land breezes, diurnal slope winds

TopographySlope, aspect towards sun, features like narrow canyons, barriers (creeks, roads, rockslides, unburnable fuel)

duff Surface litter, grass, shrubs, twigs, branches, logs

Tree crowns

FIRE

Atmospheric Dynamics

ATMOSPHEREHeat, water vapor, smoke

Fire Propagation

FIRE ENVIRONMENT

Fuel moisture

NCAR’s Coupled Atmosphere – Wildland Fire –Environment model (CAWFE)

Atmospheric Model

• 3-dim., time dependent• Nonhydrostatic, anelastic• Terrain-following coordinates,

vertically stretched grid• 2-way interacting nested

domains• Coarse grain parallelization

• Initialization of atmospheric environment using large-scale gridded weather forecast (RUC, MM5, ETA, etc.)

• Models formation of clouds, rain, and hail in “pyrocumulus” clouds over fires

• Tracks “smoke” dispersion• Aspect-dependent solar heating of

ground

Solve prognostic fluid dynamics equations of motion for air momentum, a thermodynamic variable, water vapor and precipitation on a finite difference grid.

Fire ModelEmpirical model (not PDEs). Contains components representing:

1. Surface fire:– Spread of “flaming front” depends on

wind, fuel, and slope. Based on Rothermel (1972) semi-empirical equations.

– Post-frontal heat/water vapor release2. Crown fire

– If the surface fire produces enough heat, it heats, dries, and ignites the tree canopy.

3. Heat, water vapor, and smoke fluxes released by fire into atmosphere

NCAR’s coupled atmosphere-fire model simulates the spread of a fire, the impacts

of the heat release on atmospheric motions, and the feedback of fire-induced

winds on the fire.

Big Elk Fire (4400 acres)

Pinewood Springs, CO

17 Jul 2002.

4 hr simulation.

∆x=∆y = ~50 m.

Red: 10 oC buoyancy

White: smoke

Frame each 30 sec.

W

N

Wildland Fire Modeling

Coen (2005) Intl. J. Wildland Fire

The standalone PDE based wildfire model

• Reduced chemical kinetics• Balance of heat• Balance of fuel supply• Produces a correct traveling combustion

wave

Simple Standalone PDE Fire Model

1 2 3( ) ( ) (heat balance)

( ) (fuel balance)

aT Sk T c T c T T ct tS Sf Tt

∂ ∂= −∇ ∇ + ⋅∇ − − +

∂ ∂∂

= −∂

is the temperature is the fuel supply is the reaction rate function is the ambient temperature is white noise

i

a

TSfTσ

A simple model that however exhibits the correct qualitative behavior. Not captured yet: evaporation, multiple kinds of fuel and fire, interaction with atmosphere.

Reaction and Cooling Rates

0 1000 2000 3000 4000 5000 60000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

temperature

rate

Reaction rate with offset

Reaction rate (modified Arrhenius)

Heat loss by cooling

Temperature (K)Equilibrium forced at ambient temperature

Autoignition(unstable equilibrium)

0200

400600

8001000

0

500

1000

1500

2000

2500

30000

500

1000

1500

2000

2500

x(m)

temperature

t

T(K

)

Traveling Combustion Wave 1D Simulation

time (s) space (m)

tem

pera

ture

(K)

Measured and Computed Time-Temperature Profiles

0

100

200

300

400

500

600

700

800

11250 11750 12250 12750 13250

seconds after ignition

tem

pera

ture

, C

Measured (Kremenset al, 2003)

Computed

Plane wave is used to calibrate coefficients in the model.

0 500 1000 1500 2000 2500 3000300

400

500

600

700

800

900

1000

1100

1200

t

T(K

)

Time−Temperature profile

Further development of the PDE Fire Model

•More equations for

• conservation of heat in different kinds of fire (grass, brush, crown,…)

• conservation of mass in different kinds of fuel (grass, sticks, logs…)

• conservation of water contents in the fuels (evaporation)

•Advanced finite element methods (stabilized FEM,…) for the convection-diffusion-reaction problem

•Heat fluxes (convection, radiation) between the species. Non-local radiation transfer is expensive (integral operators).

•Get wind from and exchange fluxes with an atmospheric model.

Data Acquisition

Max Elevation 5,215’Max Grade 20%Average Grade 12%

N

RT 20

RT 63

WASP project

Base map sources• Aerial photos (Nat’l High Alt.)• Gridded orthoquads• SRTM (terrain elevation)• Satellite (Landsat, QuickBird)• WASP (multispectral imaging

camera)• Fuels (AVHRR, GAP)

Data sources• Fire (GeoMAC satellite + sit.

reports/WASP/others)• Terrain (Shuttle Radar Topographic

Mission)• Meteorology - MADIS (surface

meteorology data and fuel moisture) and gridded weather forecasts

• AEDs (Temperature, winds, humidity, radiation, etc. Autonomous Environmental Detectors)

Spatial Data Sources for the Model

Wildfire Airborne Sensor Program (WASP)

High Performance Position Measurement System

Color or Color Infrared Camera• 4k x 4k pixel format• 12 bit quantization• High quality Kodak CCD

Fire Detection Cameras• 640 x 512 pixel format• 14 bit quantization• < 0.05K NEDT

•Position 5 m•Roll/Pitch 0.03 deg•Heading 0.10 deg

D. McKeownB. KremensM. Richardson

Time Sequence of Fire PropagationAerial Images from a Prescribed Burn

Image Processing Algorithms(AVIRIS Image from Vodacek et al. and Latham 2002, Int. J. Remote Sensing)

589 nm 770 nm/779 nm

Original image content• Pixel location• Spectral data• Algorithms to register to model grid

• auto extraction of tie points• affine transform

Reduced image content• Normalized Thermal Index

(MWIR-LWIR)/(MWIR+LWIR)• Fire location• Derived temperatures • Direction fire is spreading• Derived fuels (NDVI)

Autonomous Environmental Detectors (Primarily for local weather… but some burnovers)

We have developed a versatile electronic acquisition package ideally suited to field data collection

Major FeaturesReconfigure to rapidly deploy?GPS - Position AwareVersatile Data InputsVoice or Data Radio telemetryInexpensive

Kremens, et al. 2003. Int. J. Wildland Fire

Data logger and thermocouples

0

100

200

300

400

500

600

700

800

11250 11750 12250 12750 13250

seconds after ignition

tem

pera

ture

, C

Time (sec. after ignition)

T (oC)

GeoMAC Fire perimeter datahttp://www.geomac.gov

ArcIMS web application displaying current fire location.

Based on Terra MODIS fire detection products and Incident Management team uploads to Web

Data Assimilation

What are data? A meaningful data item must• Have measurement values• Have uncertainty estimate• Be related to the model state in a

known way (a.k.a. observation function)

Data item is a conditional probability density p( measurements | model state )

Data AssimilationThe standard Ensemble Kalman Filter (EnKF) approach:

• The model state is a probability distribution represented by an ensemble of simulations

– Run ensemble of simulations from initial conditions with random perturbations: how far they spread = uncertainty

– Form linear combinations by solving least squares to match data:balance the uncertainty in the prediction and the data

– Interpretation: update from the Bayes theorem assuming that the probability distributions are approximately normal => linear algebra

• The data probability distribution is represented by the measurement values and the associated error estimates

• Works well in meteorology and oceanography but fails for assimilation of data about where the fire is

Improvements of ENKF

• Standard formulas require observation matrix. It is hard enough to program to observation function. Developed a new observation matrix-free method.

• Complexity of standard formulas grows as third power of the number of data points. Developed new method with only linear complexity, making assimilation of raw images possible.

Why the Ensemble Kalman Filter fails?

• Ensemble Kalman Filters form the analysis ensemble by solving a least squares problem, trying to match the data

• The analysis ensemble is made of linear combinations of the forecast ensemble

• So, if the forecast ensemble is not rich enough, we are simply out of luck

• Even if the ensemble is rich enough, the least squares solution results often in nonphysical states

• Solutions:– Regularization: penalize by the solution gradient to prevent

nonphysical solutions– Predictor-Corrector filters to handle nongaussian distributions

and large changes of state by the Bayesian update

New EnKF technique for Fire ModelFilter developed to control the solution’s spatial gradient.

Example: 1D Fire ModelAdd quadratic form of difference between gradient of solution and gradient of ensemble mean before update solution.

i.e. Least squares fit of values and derivatives

Johns and Mandel (2005) –Envir. & Ecol. Statistics. (in print)

2D Fire Data AssimilationThe Reference solution represents the truth. Data assimilation by a standard ENKF algorithm results in an unstable solution because of the nonlinear behavior of wildfire. Stabilization gives the regularized solution ENKF+reg. Without data assimilation, the solution would develop as in the Comparison; the data assimilation shifts the model towards the truth. The model state is a probability distribution, visualized in the two ENKF figures as the superposition of transparent temperature profiles of ensemble members.

New Predictor-Corrector Ensemble Filters

Normal probability distribution does not work here

• Probability distributions (also of the solution) are too far from Gaussian• The problem is too nonlinear• Either it burns or it does not…

Probability density

Burns: 70% probability

Does not burn: 30% probability

Least squares solution: does not burn

TemperatureIgnition temperature

• Build analysis ensemble by linear combinations from an arbitrary collection of states, not just forecast ensemble

• Predictor: EnKF formulas, nudging…• Corrector: Use density estimation for

probability on infinitely dimensional spaces to assign ensemble weight to represent the analysis pdf correctly

• Independent of model dimension

Predictor-Corrector EnKF/SIS

−1.5 −1 −0.5 0 0.5 1 1.50

0.2

0.4

0.6

0.8

1

1.2

1.4EnKF

−1.5 −1 −0.5 0 0.5 1 1.50.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45Prior distribution

−1.5 −1 −0.5 0 0.5 1 1.50

1

2

3

4

5

6

7

8EnKF SIS

−1.5 −1 −0.5 0 0.5 1 1.50

1

2

3

4

5

6Data likelihood

EnKF

Predictor

Data

Forecast

SIS

Proposal AnalysisCorrector

Images from an actual numerical experiments with 100000 dofs

Concluding Remarks

High Performance Computing Requirements

• Ensemble members run on single CPUs, SMP nodes, or clusters of nodes (future)

• Linked together by massively parallel dense linear algebra

• Toy models: >100 CPUs @ >200s MB each, hours of wall clock time (BlueGene)

• Real models: >100 SMP nodes @ >4GB each (TeraGrid) >1000 nodes with less memory (BlueGene, future)

• Disk data generated: >100 GB – many TB

The Challenges

In progressNew predictor-corrector ensemble filters

Strongly nongaussian, probability distributions, sparse data

In progressTime-space ensemble filterOut of order data

ContinuousModular programming, software and data repository, build up complexity gradually

Coordinating Team software development, software reliability

DoneNew EnKF formulas with matrix-free observation function

No observation matrix (would add software complexity)

DoneNew EnKF formulas with linear complexity in data size, massively parallel linear algebra

Slow EnKF for large data sets (e.g., images)

DoneNew regularized EnKFFilter+simulations diverge because of nonlinearity

In progressEncapsulate in ensemble Kalmanfilter

Legacy code

In progressHierarchical modelingHigh fidelity simulation slow

StatusResponseChallenge

Conclusion

• Dynamic Data Driven Application System for wildfire modeling and prediction in progress

• Highly nonlinear system poses unique challenges in data assimilation and motivates new developments in data assimilation methodology

• Practical needs drive new mathematical methods• Collaborative software development• Emphasis on software validation and reliability

Without reliable software, all is just a fantasy.