Establishing Links between Atmospheric Dynamics and
Non-Gaussian Distributions and Quantifying Their Effects on Numerical Weather
Prediction
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 (Steven.Fletcher@colostate.edu)
Goal:
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.
Results:
Sample result from Kliewer et al. 2016:
References:
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.