Abstract
Weather prediction models currently operate within a probabilistic framework for generating forecasts conditioned on recent measurements of Earth’s atmosphere. This framework can be conceptualized as one that approximates parts of a Bayesian posterior density estimated under assumptions of Gaussian errors. Gaussian error approximations are appropriate for synoptic-scale atmospheric flow, which experiences quasi-linear error evolution over time scales depicted by measurements, but are often hypothesized to be inappropriate for highly nonlinear, sparsely observed mesoscale processes. The current study adopts an experimental regional modeling system to examine the impact of Gaussian prior error approximations, which are adopted by ensemble Kalman filters (EnKFs) to generate probabilistic predictions. The analysis is aided by results obtained using recently introduced particle filter (PF) methodology that relies on an implicit nonparametric representation of prior probability densities—but with added computational expense. The investigation focuses on EnKF and PF comparisons over monthlong experiments performed using an extensive domain, which features the development and passage of numerous extratropical and tropical cyclones. The experiments reveal spurious small-scale corrections in EnKF members, which come about from inappropriate Gaussian approximations for priors dominated by alignment uncertainty in mesoscale weather systems. Similar behavior is found in PF members, owing to the use of a localization operator, but to a much lesser extent. This result is reproduced and studied using a low-dimensional model, which permits the use of large sample estimates of the Bayesian posterior distribution. Findings from this study motivate the use of data assimilation techniques that provide a more appropriate specification of multivariate non-Gaussian prior densities or a multiscale treatment of alignment errors during data assimilation.
Significance Statement
Numerical predictions of Earth’s atmosphere require computer models, which represent known physical processes governing the evolution of atmospheric flow, and a clever use of statistical methods to construct a complete model representation of the true atmosphere from incomplete measurements. The second requirement is built on assumptions for the shape of error distributions for variables that are input into the model for generating predictions. The present study explores the fidelity of these error assumptions for regional weather forecasting using a novel technique that avoids common approximations that go into operational weather prediction systems.
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