Empirical RO Uncertainty Estimates Based on Signal Spectra
Presenter:
Christian Marquardt
EUMETSAT
EUMETSAT
Poster
The calculation of dynamical uncertainty estimates of bending angle data from radio occultation soundings exploiting the spectral characteristics of the measurement was proposed initially by Hocke et al. (1999) and applied in the framework of modern wave optics algorithms like the Canonical Transform by Gorbunov et al. (2006). The idea recently received renewed attention when Liu et al. (2018) presented their concept of “Local Spectral Width” as quality control and dynamical measurement uncertainty estimate in COSMIC RO data assimilation in the tropical lower troposphere.
We review the theoretical basis of the approach and propose a scaling which allows making different definitions - such as Liu’s Local Spectral Width and Gorbunov’s second-moment definition of a similar quantity - compatible with the Gaussian error variance used in data assimilation. It turns out that the selection of the window function used during the calculation of the energy distribution of the RO signal in the impact parameter/bending angle space has a significant impact on the estimated spectral width. For example, for energy distributions calculated with the widely known Short-Term Fourier Transform (STFT), we will argue that for most reasonable windowing choices, the estimated spectral width is mostly determined by the window rather than the actual local bandwidth of the signal. STFT-based local spectral widths estimates are thus not well suited or providing realistic uncertainty estimates for bending angle data unless the latter is significantly affected by impact multipath. Therefore, such methods do not offer a generic uncertainty estimate of RO measurements, but at most a heuristic approach for discovering the said impact multipath situations. While this is in line with their use in quality control applications, we propose the local Renyi entropy as a more simple-to-use diagnostic for this purpose.
As possible alternatives for obtaining generic uncertainty estimates, we analyse the use of reassigned and synchro-squeezed signal power density estimates (e.g., Auger et al., 2013) as well as an amplitude-based estimate (Cohen and Lee, 1988) for calculating the local bandwidth of RO signals. While “uncertainty” estimates obtained with these methods appear to be more plausible at first, we will finally remind ourselves that what we usually relate to uncertainty - random statistical noise - regularly appears as a noise floor in power density distributions, but does not affect spectral line width.
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