On the Measurement and Potential Applications of Non-Rayleigh Signal Statistics to Studies of Clouds and Rain

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One of the basic assumptions in radar meteorology is that the signal statistics for the amplitudes of waves scattered by distributed targets such as clouds or rain are described accurately by Rayleigh statistics. This assumption was first challenged in the 1970's on a theoretical basis, with some observational evidence following in the 1980's. In the 1990's, Jameson and his collaborator Kostinski developed an alternative theoretical basis to quantify the impact of non-Rayleigh statistics on radar measurements, and questioned the earlier observational evidence for non-Rayleigh signal statistics, arguing that it rested on an assumption of an erroneous physical model. Work under this two-component grant will extend the principal investigator's work to 1) quantify, from observations, the extent and magnitude to which non-Rayleigh signal statistics impact radar measurements, and 2) investigate means to exploit such deviations to improve our understanding of the physical systems observed. Time-series data from different radars, using normal scanning procedures, will be collected to document deviations from Rayleigh signal statistics. Observations under a variety of meteorological conditions and scanning procedures will allow the investigator to explore the magnitude and potential effects on radar measurements as well as ways to characterize and/or mitigate the same. In the second component the PI will develop the theory and measurement approach for useful observations of clustering in rain using correlated pulse samples and non-Rayleigh signal statistics, and explore potential applications to the study of spatial structures in precipitation, with a view towards improving numerical models of rain and/or snow evolution. Broader Impacts: The foremost contribution of this work will be to improve our understanding of uncertainties in precipitation radar measurements, the interpretation of which rest on Rayleigh statistical theory. The expression of the uncertainty in the measurement is critical for quantitative applications such as rainfall estimation. Conditions under which deviations from Rayleigh statistical theory may be expected do exist in large parts of precipitation systems, yet their impact on the measurements have not been quantified.