Environmental prediction centers routinely use numerical models to forecast various components of the Earth system, ranging from the geosphere to the atmosphere. Despite the diversity in applications, these models share two common characteristics, namely, they rely on physical laws to govern the time-rate-of-change of prognostic state variables and data assimilation guides how measurements inform estimates of initial conditions, boundary conditions, or unknown model parameters. The relative skill of model forecasts (e.g., comparisons of two or more global weather prediction systems) is often dominated by algorithmic choices made for data assimilation, which can be further traced back to assumptions made in priors and likelihoods used when formulating such methods from Bayes’ theorem. This seminar will focus more narrowly on atmospheric applications and discuss major obstacles to performing data assimilation with current high-resolution weather models. We will discuss the limitations of Gaussian approximations that are typically made for prior probability densities and exploit the flexibility of “particle filters,” which avoid such approximations. We will also explore the use of kernel-estimated likelihood functions trained from data accumulated during data assimilation and regime-dependent likelihoods represented using kernel embeddings of conditional distributions. These approaches allow for non-Gaussian estimates of likelihood functions that can be used directly by particle filters—or used to compute expectations of bias and error covariance for Gaussian-based data assimilation. Of equal importance, this methodology scales well for high dimensional applications, which are needed for capturing error dependence across observations. The end result is a data assimilation approach that is entirely “non-parametric” in that none of the required error distributions follow specific “shapes” determined by parameters (e.g., mean and covariance for a Gaussian). Beyond weather applications, we will discuss the theoretical advantages of fully non-parametric data assimilation for coupled Earth system models, which require accurate state estimates for the ocean, sea ice, and other component systems.
Dr. Jon Poterjoy is an Assistant Professor at the University of Maryland (UMD) Department of Atmospheric and Oceanic Science (AOSC), where he leads a research group that focuses on uncertainty quantification for geophysical systems, new data assimilation methodology, and coupled atmosphere/ocean/cryosphere modeling. Before joining UMD, Jon was a National Research Council postdoc fellow at the NOAA Atlantic Oceanic and Meteorological Laboratory and an Advanced Study Program postdoc fellow at the National Center for Atmospheric Research. Jon also held a postdoc position at the University of Oklahoma/NOAA Cooperative Institute for Mesoscale Meteorological Studies, where he worked with scientists at the NOAA National Severe Storms Laboratory. He has a Ph.D. in Meteorology from the Pennsylvania State University and a B.S. in Applied Mathematics and Meteorology from Millersville University.
