University of Colorado at Denver and Health Sciences Center Construction of a Level Function for Fireline Data Assimilation

A new method is described for determining the values of the level function from a given interface that is to be represented exactly as the zero level set. The level function is linear on boundary segments of the grid cells, which precludes the definition of the level function on the grid nodes as the signed distance from the interface. Instead, the values of the level function on a strip along the interface are found by solving a constrained least squares problem. The level function is then continued by a nearest neighbor algorithm, or a fast marching method can be used. The method was applied to representation of the burning region and of the fireline from a wildfire simulation code. Unlike other descriptions of interfaces, level set representations can be easily combined by forming linear combinations. This is useful in data assimilation methods, which modify the state of running simulation to match the data.