Basic Convective and Mesoscale Research
Other Agency – Mesoscale Dynamics and Mesoscale Applications of Information Theory
Funding Type: NSF, Office of Naval Research, FAA, NSSL Director’s Discretionary Research Fund
Objectives
Explore various instability mechanisms that will provide possible explanations
for initiation of some observed mesoscale rainbands and severe storm
elements embedded in frontal rainbands, including but not limited to
studies of modal and non-modal growths and structures in the presence
of symmetric stability and instability.
Accomplishments
The relative entropy is compared with the previously used Shannon entropy
difference as a measure of the amount of information extracted from
observations by an optimal analysis in terms of the changes in the
probability density function (pdf) produced by the analysis with respect
to the background pdf. It is shown that the relative entropy measures
both the signal and dispersion parts of the information content from
observations, while the Shannon entropy difference measures only the
dispersion part. When the pdfs are Gaussian or transformed to Gaussian,
the signal part of the information content is given by a weighted inner-product
of the analysis increment vector and the dispersion part is given by
a non-negative definite function of the analysis and background covariance
matrices. When the observation space is transformed based on the singular
value decomposition of the scaled observation operator, the information
content becomes separable between components associated with different
singular values. Densely distributed observations can be then compressed
with minimum information loss by truncating the components associate
with the smallest singular values. The differences between the relative
entropy and Shannon entropy difference in measuring information content
and information loss are analyzed in details. Illustrative examples
are given for the velocity observations from the NSSL phased array
radar with the background field from the Navy’s Coupled Ocean/Atmosphere
Mesoscale Prediction System.
This project is ongoing.
Publications
Xu, Q., 2007: Modal and non-modal symmetric perturbations. Part 1. Modal solutions
and partial orthogonality. J. Atmos. Sci., 64, 1745-1763.
Xu, Q., 2007: Measuring information content from observations for data assimilation: Relative entropy versus Shannon entropy difference. Tellus, 59A, 198-209.
Xu, Q., T. Lei, and S. Gao, 2007: Modal and non-modal