  Tropical cyclones present a serious threat to many coastal communities around
the world. Many numerical weather prediction models provide deterministic
forecasts with limited measures of their forecast uncertainty. Standard
postprocessing techniques may struggle with extreme events or use a 30-day
training window that will not adequately characterize the uncertainty of a
tropical cyclone forecast. We propose a novel approach that leverages
information from past storm events, using a hierarchical model to quantify
uncertainty in the spatial correlation parameters of the forecast errors
(modeled as Gaussian processes) for a numerical weather prediction model. This
approach addresses a massive data problem by implementing a drastic dimension
reduction through the assumption that the MLE and Hessian matrix represent all
useful information from each tropical cyclone. From this, simulated forecast
errors provide uncertainty quantification for future tropical cyclone
forecasts. We apply this method to the North American Mesoscale model forecasts
and use observations based on the Stage IV data product for 47 tropical
cyclones between 2004 and 2017. For an incoming storm, our hierarchical
framework combines the forecast from the North American Mesoscale model with
the information from previous storms to create 95\% and 99\% prediction maps of
rain. For six test storms from 2018 and 2019, these maps provide appropriate
probabilistic coverage of observations. We show evidence from the log scoring
rule that the proposed hierarchical framework performs best among competing
methods.
