The spread of invasive species can have far-reaching environmental and ecological consequences. Understanding invasion spread patterns and the underlying process driving invasions are key to predicting and managing invasions. - We combine a set of statistical methods in a novel way to characterize local spread properties and demonstrate their application using simulated and historical data on invasive insects. Our method uses a Gaussian process fit to the surface of waiting times to invasion in order to characterize the vector field of spread. - Using this method, we estimate with statistical uncertainties the speed and direction of spread at each location. Simulations from a stratified diffusion model verify the accuracy of our method. - We show how we may link local rates of spread to environmental covariates for two case studies: the spread of the gypsy moth (Lymantria dispar), and hemlock woolly adelgid (Adelges tsugae) in North America. We provide an R-package that automates the calculations for any spatially referenced waiting time data. © 2019 The Author(s) Published by the Royal Society. All rights reserved.