Data assimilation periodically adjusts the model state to incorporate new data using statistical methods. Because fire is highly nonlinear and irreversible, data assimilation for fire models poses special challenges, and standard methods, such as the ensemble Kalman filter (EnKF) do not work well. Statistical variability of corrections and especially large corrections may result in nonphysical states, which tend to be preceded or accompanied by large spatial gradients. In order to ease this problem, the regularized EnKF penalizes large changes of spatial gradients in the Bayesian update in EnKF. The regularization technique has a stabilizing effect on the simulations in the ensemble but it does not improve much the ability of the EnKF to track the data: The posterior ensemble is made out of linear combinations of the prior ensemble, and if a reasonably close location and shape of the fire cannot be found between the linear combinations, the data assimilation is simply out of luck, and the ensemble cannot approach the data. From that point on, the ensemble evolves essentially without regard to the data. This is called filter divergence. So, there is clearly a need to adjust the simulation state by a position change rather than an additive correction only. The morphing EnKF combines the ideas of data assimilation with image registration and morphing to provide both additive and position correction in a natural manner, and can be used to change a model state reliably in response to data.
