The inverse model in our approach is data assimilation. Data assimilation refers to an estimation process for time-evolving physical systems by systematic integration of the observations and computational model simulation and observations. It usually iterates an assimilation window that consists of two steps: i) a forecast step, in which a single or multi computational models make forecast to estimate the future state; and ii) an analysis step, in which the model forecast is combined with the observations taken over the corresponding time window. The result of the analysis step is the new and improved estimation, which will then used to make better forecast in the next assimilation window (Figure 1). Advanced data assimilation methods not only estimate the state but also uncertainty as well as parameters involved in the data assimilation process. Numerical weather prediction is one of most familiar applications (Figure 2).

Data assimilation is complex, interdisciplinary science with foundation in natural science, computational sciences, mathematics, and engineering. Application areas are growing rapidly, including wildfire.

Figure 2: Numerical weather prediction is one of most familiar applications of data assimilation. Credit: NOAA EMC