1
0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 x (m) 50 78 106 134 162 190 0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 0 0.4 0.8 1.2 1.6 2 x (m) 1 2 3 4 5 6 7 8 9 0.1 0.2 0.3 0.4 0.5 0.6 !""#$#%&'#() +,+%- + 0 10 20 30 40 50 60 0.05 0.1 0.15 0.2 0.25 0.3 * 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 0 0.4 0.8 1.2 1.6 2 x (m) y (m) Towards datadriven simula2ons of wildfire spread using ensemblebased data assimila2on M. Rochoux 1,2 , JM. Bart 1 , S. Ricci 1 , B. Cuenot 1 , A. Trouvé 3 1 CERFACS / CNRSURA1875, Toulouse, France. An eye on wildfire spread modeling 2 Ecole Centrale Paris, ChâtenayMalabry, France. 3 Dept. of Fire ProtecNon Engineering, University Rochoux et al., Proc. Combust. Inst., 34, in press ➡ Fundings !"#$% '(%) #* +,")(- Γ ./"$% 1. Flamescale CFD (research) ‣ Detailed simulaNons of the mechanisms underlying fire spread. ➡ MulNphysics mulNscales problem: complex interacNons of pyrolysis, combusNon and flow dynamics, atmospheric dynamics. 2. Regionalscale operaNonal model ‣ Fire spread described as a 1D front line spreading. 2 1 ➡ contact: [email protected] ➡ Objec2ve: Reduce uncertainNes in the rate of fire spread model ‣ Coupling of pyrolysis, combusNon and flow dynamics processes. ‣ High computaNonal cost. • PredicNve capability of the fire spread simulaNons. • CompaNbility with operaNonal framework. ➡ Issues: Burnt fuel Radiation Flame Wind Pyrolysis Slope ‣ Model of rate of spread (Rothermel, 1972): empirical funcNon of a reduced number of parameters • wind • slope • fuel layer depth • fuel moisture content • fuel parNcle S/A • ANR09COSI006 IDEA • LEFEASSIM (INSU) Data assimilaNon algorithm ➡ Principles: integrate observaNons of fire front locaNons into a fire spread computaNonal model ➡ Fire spread model ‣ Levelset front tracking technique. ‣ Progress variable c as flame marker. ∂ c ∂ t = Γ|∇c| • account for the effects of both observaNon and modeling errors. • esNmate opNmal set of parameters in the rate of spread model (inverse problem). Model feedback Γ !"#$% '#()*#$ c =0 c =1 c fr =0.5 2. StochasNc computaNon of the covariance matrices and (accounNng for non lineariNes in the fire spread model). ➡ Ensemble Kalman Filter (EnKF) algorithm !"#$%&'()*# ,)*-%). /'%'0$-$%# 1203.'()*# 42%$ #/%$'5 0)5$. 6*#$0".$ 7'.0'* 42.-$% '.8)%2-90 " y o x − x + H (x − ) x − x − 4. ArNficial parameter evoluNon (Moradkhani, 2005). 1. Monte Carlo basedtechnique: predicted fire front posiNons associated with ensemble of prior parameters (members). x + = x − + C xy C yy + C y o y o y o + ξ − H (x − ) C xy C yy ➡ Allow for a temporal correcNon of the model parameters 3. CalculaNon of retrospecNve posterior esNmates of the control parameters . x + Results: Datadriven wildfire spread model ➡ STEP.1 ValidaNon: syntheNc observaNons generated using specified values of the coefficient P (case in which the true Nmevarying value of P is known) ‣ ObservaNon generated each 50 s. ‣ 1parameter esNmaNon ‣ Fire igniNon as a circular front. ‣ Rate of spread > 1 cm/s. true prior posterior true CYCLE 1 prior posterior ➡ STEP.2 Controlled grassland fire under moderate wind condiNons (R. Paugam, King’s College of London): fire front observaNons extracted from thermal infrared imaging. ‣ 4parameter esNmaNon (1024 members) ‣ Rate of spread ~ 1 cm/s. ‣ ObservaNon error: 5 cm (camera spaNal resoluNon). 48 members • observaNons ASSIMILATION (t = 78 s) prior posterior DATA: arrival Nmes (s) t = 78 s • ReducNon of the uncertainty on forecast. • Bejer tracking of the observed fronts. ➡ Result: Improvement of the forecast fire front posiNon • Physical parameters stay within physical range. • Polynomial Chaos approach Ongoing research • Extension of the control vector to the posiNons of the fire front. ‣ Use a surrogate model of the observaNon operator to reduce the computaNonal cost of the EnKF algorithm. • ApplicaNon to more realisNc cases of fire spread. ObservaNon error standard deviaNon (m) Mean of the posterior esNmates (1/s) σ o 9 CYCLES 48 members =5m σ o AssimilaNon cycle Mean of the posterior esNmates (1/s) FORECAST (t = 106 s) !"#$%&'() +,-./0&'() 1(/#&% 2"/.3'() ‣ OSSE framework ‣ VegetaNon layer thickness ~ 1 m σ b = 0.05 s 1 t = 106 s u w Σ M f Γ = P u w , α sl ,M f , Σ δ
