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Wildland fires pose an increasingly serious problem in our society. The number and severity of these fires has been rising for many years. Wildfires pose direct threats to life and property as well as threats through ancillary effects like reduced air quality. The aim of this thesis is to develop techniques to help combat the impacts of wildfires by improving wildfire modeling capabilities by using satellite fire observations. Already much work has been done in this direction by other researchers. Our work seeks to expand the body of knowledge using mathematically sound methods to utilize information about wildfires that considers the uncertainties inherent in the satellite data. In this thesis we explore methods for using satellite data to help initialize and steer wildfire simulations. In particular, we develop a method for constructing the history of a fire, a new technique for assimilating wildfire data, and a method for modifying the behavior of a modeled fire by inferring information about the fuels in the fire domain. These goals rely on being able to estimate the time a fire first arrived at every location in a geographic region of interest. Because detailed knowledge of real wildfires is typically unavailable, the basic procedure for developing and testing the methods in this thesis will be to first work with simulated data so that the estimates produced can be compared with known solutions. The methods thus developed are then applied to real-world scenarios. Analysis of these scenarios shows that the work with constructing the history of fires and data assimilation improves improves fire modeling capabilities. The research is significant because it gives us a better understanding of the capabilities and limitations of using satellite data to inform wildfire models and it points the way towards new avenues for modeling fire behavior.