The prevalence and severity of Wildland-Urban Interface (WUI) fires is on the rise globally. Wildfires that spread into urban areas are known as WUI fires, with firebrand exposure a leading cause of structure losses during these WUI fire events. However, the complex ignition process of WUI building materials by glowing firebrand piles has not been fully resolved. The objective of this research was to develop a numerical ignition model capable of predicting the ignition probability of any horizontally-mounted flammable substrate when exposed to a pile of glowing firebrands. This development process was based on: extensive experimental data quantifying the mechanisms controlling the ignition process; a novel empirical firebrand pile heat flux model; and comprehensive pyrolysis models of three commonly-used lignocellulosic building materials.Experiments were conducted in a bench-scale wind tunnel where a glowing firebrand pile of controlled geometry was deposited onto a horizontally-mounted substrate. Forced air flow velocities in the range of 0.9 – 2.7 m s-1 and two firebrand pile coverage densities (0.06 and 0.16 g cm-2) were used, significantly expanding the range of conditions used in earlier laboratory-scale studies. The firebrand pile thermal exposure and burning intensity were quantified using time-resolved back surface temperature and combustion heat release rate data. Flammable substrate flaming ignition and extinction statistics, as well as burning intensity data, were also collected. A custom inverse heat flux modeling technique, utilizing a solid-phase pyrolysis solver, ThermaKin, and infrared thermal imaging back surface temperature data, was employed to generate incident firebrand pile heat flux profiles directly underneath and in front of a glowing firebrand pile. The time-dependent firebrand pile heat flux behavior was captured using a three-step piecewise linear function. Further, a novel empirical firebrand pile heat flux model was developed, capable of generating time-dependent firebrand pile heat flux profiles over a range of forced air flows (0 – 4 m s-1) and for all firebrand pile coverage densities and geometries. A hierarchical modeling approach was used to develop a comprehensive pyrolysis model for each lignocellulosic substrate through inverse analysis of milligram- and gram-scale experimental data. All relevant kinetics, thermodynamics, and thermal transport properties of pyrolysis was parameterized. Finally, a novel numerical ignition model used to predict the ignition probability of any flammable target substrate when exposed to a glowing firebrand pile under wind was developed. A newly-defined dimensionless flame stability parameter was used as a material-independent criterion to characterize the ignition of a flammable substrate surface. The model captured the stochastic ignition behavior of flammable substrates by firebrand piles, as well as the reduced burning intensity of the piles deposited onto a flammable substrate surface. A logistic growth function was found to most accurately capture the ignition probability dependence on the dimensionless flame stability parameter and was, on average, capable of predicting the ignition probability within 14% of the experimental data. Further, using a critical dimensionless flame stability parameter, the absolute average difference between all experimental and predicted ignition timing and burning duration data was 11 and 26 s respectively.