Kirkwood Distribution Function and its Application for the Analysis of Radio Occultation Observations
Presenter:
M.E. Gorbunov (1,2)
(1) A.M.Obukhov Institute of Atmospheric Physics Russian Academy of Sciences, Moscow, Russia (2) Wegener Center for Climate and Global Change, University of Graz, Graz, Austria
(1) A.M.Obukhov Institute of Atmospheric Physics Russian Academy of Sciences, Moscow, Russia (2) Wegener Center for Climate and Global Change, University of Graz, Graz, Austria
Poster
The Wigner Distribution Function (WDF) was introduced very early during the development of quantum mechanics. It appeared in works by Wigner, Dirac, Weyl, and Heisenberg, who derived it from the wave energy density operator and re-formulated quantum mechanics in terms of the classical phase space. Later, it was also used in signal processing and was as well applied to the analysis of Radio Occultation (RO) observations. WDF unfolds a one-dimensional signal, or a function of time, in the time-frequency plane and allows decomposing a signal into multiple quasi-monochromatic tones, i.e., signals with slowly changing amplitude and frequency. This property made it useful for the analysis of RO signals in multi-path zones. Less known is the Kirkwood Distribution Function (KDF), which was also introduced in quantum mechanics in the same time period as WDF. WDF and KDF have some common properties. Both asymptotically tend to a delta-like distribution concentrated on the ray manifold. They, however, also exhibit some differences. While WDF numerical evaluation requires significant computation costs, KDF evaluation is exceptionally easy and only requires a single (large) Fast Fourier Transform. However, the use of KDF is not that straightforward: unlike WDF, the amplitude of which directly visualizes the ray manifold shape, KDF utilizes the phase relations only: its stationary point lies at the ray manifold and, in proportion to the distance from the ray manifold, its oscillation frequency increases. In this work, we study the utility of the KDF for RO observations. We give examples of processing real RO events, with the evaluation of both WDF and KDF, and discuss the possible advantages of the latter.
Poster in PDF:
