Oriol Rios, Wolfram Jahn, Guillermo Rein

Forecasting Wind-Driven Wildfires Using An Inverse Modelling Approach

Cargèse, 16-5-2013

Numerical Wildfires Workshop

Outline

Background idea

Methodology

– Forward model

– Optimization. Tangent lineal model & automatic differentiation

– Synthetic validation

Cases explored

– Fire fronts

– Wind speed

– Wind speed and direction

– Fuel depth

Perturbed data

Conclusions & Further Work2

Background Idea

Hard to gather information to initialize models in operative situations

Complex model require high computational capacity and time

Wildfire responders need forecasting tools

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M. Rochoux et al., J. Mandel et al. started using data assimilation in wildfires

La Riba, 2011La Jonquera, 2011

Background Idea

Jahn et al. successfully used DA to forecast fire in compartments

The algorithm is based on the fact that invariants exists for a certain amount of time

W. Jahn et al. Forecasting fire dynamics using inverse computational fluid dynamics

and tangent linearisation, Advances in Engineering Software4

ex: Entrainment coefficient

Background Idea

Invariants exists and represent one or more physical quantities (i.e. wind speed or fuel properties).

Use a simple yet reliable model to explore DA capacities for wind-driven wild fires.

Versatile DA algorithm regarding available data (invariants reversibility)

Ensure positive lead time

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Input fire fronts positions (airborne, satellite) during an assimilation window to identify the invariants

min.

Data

Forward model

Invariants

Source of data

6La Jonquera, 2011

CSIRO-UPC, 2008FuSE project - Bushfire CRCNgarkat CP experimental burnings (SAus)

Airborne and Satellite imaged

Pléiades SATMODIS/Google

Rate of spread (surface fire)

11 variables (7+4)

variables

parameters

The forward model: Rothermel’s+Huygens

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Huygens principle. Firelets expansion

G D Richards. The properties of elliptical wildfire growth for time dependent fuel and meteorological

conditions. Combustion science and technology,1993

+ Anderson length-to-breadth correlation

The forward model: Rothermel’s+Huygens

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Generates no trivial perimeters (fuel heterogeneity)

The forward model: Rothermel’s+Huygens

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Cost function

Distance between angular correspondent vertexes

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Optimization

Tangent linear model

How to calculate the gradient?

Automatic differentiation(forward or adjoint)

Program

dProgram

aProgram11

First Guess

Optimization. Automatic differentiation

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sin(x1/x2)

Algorithm

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Validation

I used synthetically data generated with Rothermel’s+Huygens model (without casting invariants) and initialized with parameters from Behave (Anderson)

We studied 4 different invariants cast

4 invariants

3 invariants

3 invariants

3 invariants

+ wind speed

+ wind direction

+ fuel depth14

Casting the invariants. 1st cast. (4 invariants)

Moisture-fuel Invariant

Wind speed invariant

Wind factor invariant

Wind direction

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Step-to-step exampleCasting the invariants. 1st cast. (4 invariants)

What if the invariant’s evolution is known?

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Convergence to true valueCasting the invariants. 1st cast. (4 invariants)

•Influence initial guess•Divergence correction17

2nd cast of invariants: 3 invariants & wind speed

Moisture-fuel Invariant

Wind factor invariant

Wind direction

Input Data

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2nd cast of invariants: 3 invariants & wind speed

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3rd cast of invariants: 3 invariants & wind (U,θ)

Moisture-fuel Invariant

Wind factor invariant

Wind directionInput Data

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3rd cast of invariants: 3 invariants & wind (U,θ)

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4th cast of invariants: 3 invariants & fuel depth (x,y)

RoS linear to fuel depth

Wind direction

Input Data

Length to breadth ratio (Anderson)

LBI

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4th cast of invariants: 3 invariants & fuel depth (x,y)

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Data with noise (4th case)

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Computing time

Positive lead time26

Windows of validity30 min forecast

Conclusions

Formulation of the problem is general enough that is suitable to work with many observation (& data contexts).

Solution method is fast and positive lead times are already possible with desktop computer.

Invariants can be turned into input data for increased accuracy and speed if reliable data arrives

The proper invariant cast must be done according to the available data, otherwise multiplicity might be a problem.

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Further work

Challenge the algorithm with real data (cases needed)

Increase the number of invariants to several dozen by means of adjoint modeling approach

Assimilate more input data (fire intensity, flame height...)

Move to more powerful optimization routine that require High Performance Computing (eg, evolutionary algorithms)

Used more sophisticated forward models (i.e WFDS, FireFoam, ForeFire...)28

Thank you!

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Forecast made in 1900 of the fire-fighting in the year 2000.

Villemard 1910, National Library of France

Invariants range

Monte Carlo analysis varying 6 Rothermel’s variables (20000 sets) within the range established by Scott and Burgan 2005.

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Invariants influence

Cost function variation when the invariants are perturbed ±20% of its base value

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Invariants influence

Base value and varying range for Rothermel’s variables

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