A wildland fire model with data assimilation

A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients that can be approximated from prior measurements of wildfires. An ensemble Kalman filter technique with regularization is then used to assimilate temperatures measured at selected points into running wildfire simulations. The assimilation technique is able to modify the simulations to track the measurements correctly even if the simulations were started with an erroneous ignition location that is quite far away from the correct one.Comment: 35 pages, 12 figures; minor revision January 2008. Original version available from http://www-math.cudenver.edu/ccm/report

Optimal Control and Stochastic Parameter Estimation

International audienceAn efficient sampling method is proposed to solve the stochastic optimal control problem in the context of data assimilation for the estimation of a random parameter. It is based on Bayesian inference and the Markov Chain Monte Carlo technique, which exploits the relation between the inverse Hessian of the cost function and the error covariance matrix to accelerate convergence of the sampling method. The efficiency and accuracy of the method is demonstrated in the case of the optimal control problem governed by the nonlinear Burgers equation with a viscosity parameter that is a random field