Modeling Wind Uncertainties for Stochastic Trajectory Synthesis

Abstract

This paper presents a statistical model of wind forecast uncertainty for stochastic trajectory generations based on past wind forecast errors from the Rapid Update Cycle (RUC) weather prediction system. In this paper, compositions of wind uncertainties are first analyzed. Methods of nominal wind field determination are discussed next, followed by analyses of spatial and temporal correlations of wind forecast errors, their variations over geographic locations and look-ahead times, as well as their likely probabilistic distributions. Potential dependences of wind forecast errors on prominent wind field properties, such as wind magnitude, temperature, pressure, and wind gradient, are also examined. Then, a quasi-stationary, quasi-homogenous, and non-Gaussian random field model of wind forecast uncertainty is presented based on a weighted sum of historical wind forecast errors at locations and look-ahead intervals within the spatial and temporal correlation ranges of the current point of interest, plus two purely random corrections to reflect model residuals, initial measurement errors, and errors in the nominal wind determination process. Finally, the wind uncertainty model is applied to stochastic predictions of level flight trajectories, and different guidance strategies are used to examine likely dispersions of position, time of arrival, and fuel burn. Nomenclature c tsfc Thrust specific fuel consumption