Establishing Links between Atmospheric Dynamics and Non-Gaussian Distributions and Quantifying Their Effects on Numerical Weather Prediction

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Data assimilation is a method that is used to incorporate observations into a numerical model to improve the representation of the current state of the system. Data assimilation is widely used in atmospheric sciences to assist weather forecasting models, making use of data from satellites, weather stations, weather balloons and many other systems. The focus of the research in this project are the errors that arise between the observations and model state. The errors are assumed to be Gaussian, or evenly distributed, but for some variables that may not be the case. The research in this award will improve our understanding of non-Gaussian errors. The potential impact on society would be improved weather forecasting. Data assimilation is also growing in other areas of science, so the research potentially has cross-cutting applications. An early career scientist will also be trained in this growing area of research.The research team will address several different aspects about how non-Gaussian distributed errors affect data assimilation and retrieval systems, but also how to detect when the Gaussian assumption is not optimal. Research will move forward on five topics: 1) Build conditional probability density functions (PDF) for different atmospheric dynamics from forecast difference fields, as a proxy for the background error fields, and then develop mathematical and stochastical models to link the conditional PDFs to specific atmospheric dynamics, 2) Derive, test in a toy problem, and then implement into the WRF-GSI, a mixed PDF hybrid variational-ensemble system, 3) Investigate the impact of different PDF assumptions for different scales of dynamics in both retrieval and hybrid data assimilation systems, 4) Extend the lognormal detection algorithm to a near real-time capability for educational diagnostics, 5) Create web pages to illustrate the different values that the systems produce combined with the detection algorithm output as an educational tool for researchers to see the effects of the distributions on the performance of the retrievals.