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

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A 3-year NSF project to address several different aspects about how non-Gaussian distributed errors affect data assimilation (DA) and retrieval systems, and also how to detect when the Gaussian assumption is not optimal.

PI: Steve Fletcher, Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins CO (

Click Here for Latest CIRA 1DVAR Water Vapor Retrievals from ATMS (run as Gaussian, Lognormal and Transform)


1)   Develop mathematical and stochastic links by building conditional PDFs for different atmospheric dynamics from forecast difference fields, as a proxy to the background errors, and then consider Markov process model techniques, similar to those in Sardeshmukh and Penland (2015), 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.  New detection methods will also be researched that are based on machine learning, similar to Desobry et al. (2005).

5)   Create web pages, and host the three versions of the CIRA 1DVAR Optimal Estimator (C1DOE) in near real time, combined with the non-Gaussian observational quality control, 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. 


Sample result from Kliewer et al. 2016:


Desobry, F., Davy, M., and Doncarli, C., 2005:  An Online Kernel Change Detection Algorithm.  IEE Transactions on Signal Processing.  53, 2961-2974.  DOI:  10.1109/TSP.2005.851098

Kliewer, A. J., Fletcher, S. J., Jones, A. S. and Forsythe, J. M. (2016), Comparison of Gaussian, logarithmic transform and mixed Gaussian–log-normal distribution based 1DVAR microwave temperature–water-vapour mixing ratio retrievals. Q.J.R. Meteorol. Soc., 142, 274–286.

Sardeshmunk, P. D. and C. Penland, 2015: Understanding the distinctively skewed and heavy tailed character of atmospheric and oceanic probability distributions. Chaos, 25, 036410.


This material is based upon work supported by the National Science Foundation under Grant Number 1738206.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.